Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)

Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings under rotation (the cyclic group). A k-ary unlabeled necklace is an equivalence class of k-ary strings under rot...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of algorithms Ročník 37; číslo 2; s. 267 - 282
Hlavní autori: Cattell, Kevin, Ruskey, Frank, Sawada, Joe, Serra, Micaela, Miers, C.Robert
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: San Diego, CA Elsevier Inc 01.11.2000
Elsevier
Predmet:
Exact sciences and technology
Group theory
Group theory and generalizations
Mathematics
Sciences and techniques of general use
Necklace (mathematics)
Irreducible polynomial
Cyclic group
Group theory
Constant atomized time algorithm
Algorithm
Tournament
ISSN:0196-6774, 1090-2678
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings under rotation (the cyclic group). A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algorithms for generating (i.e., listing) all necklaces and binary unlabeled necklaces. These algorithms have optimal running times in the sense that their running times are proportional to the number of necklaces produced. The algorithm for generating necklaces can be used as the basis for efficiently generating many other equivalence classes of strings under rotation and has been applied to generating bracelets, fixed density necklaces, and chord diagrams. As another application, we describe the implementation of a fast algorithm for listing all degree n irreducible and primitive polynomials over GF(2).
AbstractList Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings under rotation (the cyclic group). A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algorithms for generating (i.e., listing) all necklaces and binary unlabeled necklaces. These algorithms have optimal running times in the sense that their running times are proportional to the number of necklaces produced. The algorithm for generating necklaces can be used as the basis for efficiently generating many other equivalence classes of strings under rotation and has been applied to generating bracelets, fixed density necklaces, and chord diagrams. As another application, we describe the implementation of a fast algorithm for listing all degree n irreducible and primitive polynomials over GF(2).
Author Cattell, Kevin
Miers, C.Robert
Serra, Micaela
Sawada, Joe
Ruskey, Frank
Author_xml – sequence: 1
  givenname: Kevin
  surname: Cattell
  fullname: Cattell, Kevin
  organization: HP Research Labs, Santa Rosa, California, f1kevin_cattell@hp.comf1
– sequence: 2
  givenname: Frank
  surname: Ruskey
  fullname: Ruskey, Frank
  organization: Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada
– sequence: 3
  givenname: Joe
  surname: Sawada
  fullname: Sawada, Joe
  organization: Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada
– sequence: 4
  givenname: Micaela
  surname: Serra
  fullname: Serra, Micaela
  organization: Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada
– sequence: 5
  givenname: C.Robert
  surname: Miers
  fullname: Miers, C.Robert
  organization: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canadaf2crmiers@math.uvic.caf2
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=805528$$DView record in Pascal Francis
BookMark eNp1kE1LAzEQhoMoWKtXzwEvCm6dtPuRPZZiqyDqwZ6X2WRWU9OkJLHgv3dLRUTwNMzM-wzMc8IOnXfE2LmAkQAob1b4uh6NAfpWgDxgAwE1ZOOykodsAKIus7Kq8mN2EuMKQIgirwesnWNMfGpffTDpbR158nxBjgIm4o-k3i0qitd86Sy2ZEn_HqLT_D4E0h_KtJb4s7efzq8N2sj9lgJfzC_HV6fsqOsndPZdh2w5v32Z3WUPT4v72fQhUxMJKasQsRVlRW2nC2o1CSraCQKipKLrdJ5jraUWRVlN-j2AqkWtkSpRdqXU1WTILvZ3NxgV2i6gUyY2m2DWGD4bCUUxln1qtE-p4GMM1P0EBDQ7j83OY7Pz2Ow89kD-B1AmYTLepYDG_o_JPUb9y1tDoYnKkFOkTSCVGu3Nf-gXXjONsQ
CODEN JOALDV
CitedBy_id crossref_primary_10_1007_s00009_017_1025_4
crossref_primary_10_1016_j_jaca_2025_100034
crossref_primary_10_1145_3689633
crossref_primary_10_1080_00207160_2013_805753
crossref_primary_10_1016_j_disc_2021_112780
crossref_primary_10_1016_j_aam_2018_08_005
crossref_primary_10_1016_j_jda_2017_10_002
crossref_primary_10_1016_j_jmva_2013_12_001
crossref_primary_10_1007_s10569_017_9789_1
crossref_primary_10_1016_j_ipl_2007_10_011
crossref_primary_10_1016_j_tcs_2019_01_030
crossref_primary_10_1137_15M1043248
crossref_primary_10_1016_j_jalgor_2008_10_001
crossref_primary_10_1016_j_jda_2017_01_003
crossref_primary_10_1137_S0895480100377970
crossref_primary_10_1016_j_tcs_2012_11_024
crossref_primary_10_1109_TIT_2024_3473940
crossref_primary_10_1137_S0097539700377037
crossref_primary_10_1016_j_ipl_2017_04_010
crossref_primary_10_1109_TAES_2014_120269
crossref_primary_10_1145_1125994_1125995
crossref_primary_10_1016_j_actaastro_2017_10_017
crossref_primary_10_1016_j_tcs_2012_03_048
crossref_primary_10_1016_S0196_6774_02_00286_9
crossref_primary_10_1587_transfun_E95_A_909
crossref_primary_10_1016_j_asr_2020_04_045
crossref_primary_10_1007_s12095_024_00746_7
crossref_primary_10_1088_1402_4896_adf0ee
crossref_primary_10_1016_j_jda_2014_06_003
crossref_primary_10_1016_j_actaastro_2017_02_016
crossref_primary_10_1016_j_disc_2018_09_024
crossref_primary_10_1016_S0304_3975_03_00049_5
crossref_primary_10_1007_s11334_022_00467_1
crossref_primary_10_1016_j_tcs_2020_10_034
Cites_doi 10.1016/0012-365X(78)90002-X
10.1016/0020-0190(76)90014-4
10.1007/3-540-44968-X_33
10.1145/236869.236882
10.1137/S0895480192234009
10.1016/0304-3975(94)00013-1
10.1137/S0097539798344112
10.1215/ijm/1255631587
10.1016/0196-6774(92)90047-G
10.1093/comjnl/31.3.283
10.1016/0012-365X(86)90089-0
10.1016/0304-3975(88)90113-2
10.1016/0196-6774(83)90017-2
ContentType Journal Article
Copyright 2000 Academic Press
2001 INIST-CNRS
Copyright_xml – notice: 2000 Academic Press
– notice: 2001 INIST-CNRS
DBID AAYXX
CITATION
IQODW
DOI 10.1006/jagm.2000.1108
DatabaseName CrossRef
Pascal-Francis
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
Mathematics
EISSN 1090-2678
EndPage 282
ExternalDocumentID 805528
10_1006_jagm_2000_1108
S0196677400911088
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29J
4.4
4G.
5GY
5VS
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABMAC
ABTAH
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADFGL
ADGUI
ADIYS
ADJOM
ADMUD
AEBSH
AEKER
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CAG
COF
CS3
DM4
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FA8
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBOLZ
HLZ
HMJ
HVGLF
HZ~
IHE
KOM
LG5
LX9
M25
MHUIS
MO0
MVM
N9A
O-L
O9-
OAUVE
OZT
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SBC
SDF
SDG
SDP
SEW
SME
SPC
SSV
SSW
SSZ
T5K
TN5
TWZ
UPT
UQL
WUQ
XJT
XPP
YQT
ZCA
ZU3
ZY4
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABJNI
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
CITATION
EFKBS
~HD
AFXIZ
AGCQF
AGRNS
IQODW
SSH
ID FETCH-LOGICAL-c380t-7aaab167ebfd5ebde1e5b3a0aa8e5ffd44a9d8d156735eb00c919dae716f68d73
ISICitedReferencesCount 56
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000165183500003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0196-6774
IngestDate Mon Jul 21 09:15:36 EDT 2025
Tue Nov 18 22:43:36 EST 2025
Sat Nov 29 06:24:22 EST 2025
Fri Feb 23 02:22:56 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Necklace (mathematics)
Irreducible polynomial
Cyclic group
Group theory
Constant atomized time algorithm
Algorithm
Tournament
Language English
License https://www.elsevier.com/tdm/userlicense/1.0
CC BY 4.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c380t-7aaab167ebfd5ebde1e5b3a0aa8e5ffd44a9d8d156735eb00c919dae716f68d73
PageCount 16
ParticipantIDs pascalfrancis_primary_805528
crossref_primary_10_1006_jagm_2000_1108
crossref_citationtrail_10_1006_jagm_2000_1108
elsevier_sciencedirect_doi_10_1006_jagm_2000_1108
PublicationCentury 2000
PublicationDate 2000-11-01
PublicationDateYYYYMMDD 2000-11-01
PublicationDate_xml – month: 11
  year: 2000
  text: 2000-11-01
  day: 01
PublicationDecade 2000
PublicationPlace San Diego, CA
PublicationPlace_xml – name: San Diego, CA
PublicationTitle Journal of algorithms
PublicationYear 2000
Publisher Elsevier Inc
Elsevier
Publisher_xml – name: Elsevier Inc
– name: Elsevier
References Fredricksen, Maiorana (RF6) 1978; 23
Duval (RF2) 1983; 4
Technical report, tr-rsfb-96-018, University of Paderborn, Germany, 1996.
Lidl, Niederreiter (RF14) 1994
Gilbert, Riordan (RF8) 1961; 5
Berstel, Pocchiola (RF1) 1994; 132
Proskurowski, Ruskey, Smith (RF17) 1998; 11
Er (RF4) 1988; 31
Golomb (RF10) 1967
Graham, Knuth, Patashnik (RF11) 1989
Ruskey, Sawada (RF21) 1999; 29
Proc. 6th Annual International Combinatorics and Computing Conference (CO-COON), Sydney, Australia, July 2000, Lecture Notes in Computer Science, to appear, Springer-Verlag, Berlin/New York.
Lüneburg (RF15) 1989
J. Sawada, Generating bracelets in constant amortized time, manuscript, 1999.
von zur Gathen, Gerhard (RF24) 1996
Golomb (RF9) 1967; 4
J. von zur Gathen, and, J. Gerhard, Arithmetic and Factorization of Polynomials over
Kaye (RF12) 1976; 5
Lothaire (RF16) 1983
Knuth (RF13) 1992; 606
Fredricksen, Kessler (RF5) 1986; 61
Ruskey, Savage, Wang (RF20) 1992; 13
F. Ruskey, and, J. Sawada, Generating necklaces and strings with forbidden substrings
Duval (RF3) 1988; 60
Reutenauer (RF18) 1993
F. Ruskey, Combinatorial generation, manuscript, course notes for CSC 528, Univ. Victoria, 1995.
von zur Gathen (10.1006/jagm.2000.1108_RF24) 1996
Duval (10.1006/jagm.2000.1108_RF2) 1983; 4
Graham (10.1006/jagm.2000.1108_RF11) 1989
Lothaire (10.1006/jagm.2000.1108_RF16) 1983
Duval (10.1006/jagm.2000.1108_RF3) 1988; 60
10.1006/jagm.2000.1108_RF7
10.1006/jagm.2000.1108_RF19
10.1006/jagm.2000.1108_RF23
Gilbert (10.1006/jagm.2000.1108_RF8) 1961; 5
10.1006/jagm.2000.1108_RF22
Er (10.1006/jagm.2000.1108_RF4) 1988; 31
Lüneburg (10.1006/jagm.2000.1108_RF15) 1989
Fredricksen (10.1006/jagm.2000.1108_RF5) 1986; 61
Ruskey (10.1006/jagm.2000.1108_RF21) 1999; 29
Kaye (10.1006/jagm.2000.1108_RF12) 1976; 5
Fredricksen (10.1006/jagm.2000.1108_RF6) 1978; 23
Lidl (10.1006/jagm.2000.1108_RF14) 1994
Proskurowski (10.1006/jagm.2000.1108_RF17) 1998; 11
Golomb (10.1006/jagm.2000.1108_RF10) 1967
Knuth (10.1006/jagm.2000.1108_RF13) 1992; 606
Reutenauer (10.1006/jagm.2000.1108_RF18) 1993
Golomb (10.1006/jagm.2000.1108_RF9) 1967; 4
Berstel (10.1006/jagm.2000.1108_RF1) 1994; 132
Ruskey (10.1006/jagm.2000.1108_RF20) 1992; 13
References_xml – reference: F. Ruskey, and, J. Sawada, Generating necklaces and strings with forbidden substrings,
– volume: 4
  year: 1967
  ident: RF9
  publication-title: Irreducible Polynomials, Synchronization Codes, Primitive Necklaces, and the Cyclotomic Algebra
– volume: 11
  start-page: 94
  year: 1998
  end-page: 109
  ident: RF17
  article-title: Analysis of algorithms for listing equivalence classes of
  publication-title: SIAM J. Discrete Math.
– year: 1989
  ident: RF15
  publication-title: Tools and Fundamental Constructions of Combinatorial Mathematics
– year: 1994
  ident: RF14
  publication-title: Introduction to Finite Fields and Their Applications
– reference: J. von zur Gathen, and, J. Gerhard, Arithmetic and Factorization of Polynomials over
– volume: 4
  start-page: 363
  year: 1983
  end-page: 381
  ident: RF2
  article-title: Factoring words over an ordered alphabet
  publication-title: J. Algorithms
– reference: J. Sawada, Generating bracelets in constant amortized time, manuscript, 1999.
– volume: 23
  start-page: 207
  year: 1978
  end-page: 210
  ident: RF6
  article-title: Necklaces of beads in
  publication-title: Discrete Math.
– volume: 60
  start-page: 255
  year: 1988
  end-page: 283
  ident: RF3
  article-title: Génération d'une section des classes de conjugaison et arbre des mots de Lyndon de longueur bornée
  publication-title: Theoret. Comput. Sci.
– year: 1983
  ident: RF16
  publication-title: Combinatorics on Words
– volume: 5
  start-page: 171
  year: 1976
  end-page: 173
  ident: RF12
  article-title: A Gray code for set partitions
  publication-title: Inform. Process. Lett.
– reference: , Technical report, tr-rsfb-96-018, University of Paderborn, Germany, 1996.
– year: 1967
  ident: RF10
  publication-title: Shift Register Sequences
– reference: F. Ruskey, Combinatorial generation, manuscript, course notes for CSC 528, Univ. Victoria, 1995.
– volume: 606
  year: 1992
  ident: RF13
  publication-title: Axioms and Hulls
– reference: , Proc. 6th Annual International Combinatorics and Computing Conference (CO-COON), Sydney, Australia, July 2000, Lecture Notes in Computer Science, to appear, Springer-Verlag, Berlin/New York.
– volume: 13
  start-page: 414
  year: 1992
  end-page: 430
  ident: RF20
  article-title: Generating necklaces
  publication-title: J. Algorithms
– year: 1993
  ident: RF18
  publication-title: Free Lie Algebras
– volume: 29
  start-page: 671
  year: 1999
  end-page: 684
  ident: RF21
  article-title: An efficient algorithm for generating necklaces with fixed density
  publication-title: SIAM J. Comput.
– year: 1996
  ident: RF24
  article-title: Arithmetic and factorization of polynomials over
  publication-title: Proc. ISSAC 96
– year: 1989
  ident: RF11
  publication-title: Concrete Mathematics
– volume: 132
  start-page: 415
  year: 1994
  end-page: 425
  ident: RF1
  article-title: Average cost of Duval's algorithm for generating Lyndon words
  publication-title: Theoret. Comput. Sci.
– volume: 31
  start-page: 283
  year: 1988
  end-page: 284
  ident: RF4
  article-title: A fast algorithm for generating set partitions
  publication-title: Comput. J.
– volume: 61
  start-page: 181
  year: 1986
  end-page: 188
  ident: RF5
  article-title: An algorithm for generating necklaces of beads in two colors
  publication-title: Discrete Math.
– volume: 5
  start-page: 657
  year: 1961
  end-page: 665
  ident: RF8
  article-title: Symmetry types of periodic sequences
  publication-title: Illinois J. Math.
– volume: 4
  year: 1967
  ident: 10.1006/jagm.2000.1108_RF9
– volume: 23
  start-page: 207
  year: 1978
  ident: 10.1006/jagm.2000.1108_RF6
  article-title: Necklaces of beads in k colors and k-ary de Bruijn sequences
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(78)90002-X
– volume: 5
  start-page: 171
  year: 1976
  ident: 10.1006/jagm.2000.1108_RF12
  article-title: A Gray code for set partitions
  publication-title: Inform. Process. Lett.
  doi: 10.1016/0020-0190(76)90014-4
– ident: 10.1006/jagm.2000.1108_RF23
– ident: 10.1006/jagm.2000.1108_RF22
  doi: 10.1007/3-540-44968-X_33
– ident: 10.1006/jagm.2000.1108_RF7
  doi: 10.1145/236869.236882
– volume: 11
  start-page: 94
  year: 1998
  ident: 10.1006/jagm.2000.1108_RF17
  article-title: Analysis of algorithms for listing equivalence classes of k-ary strings induced by simple group actions
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/S0895480192234009
– volume: 132
  start-page: 415
  year: 1994
  ident: 10.1006/jagm.2000.1108_RF1
  article-title: Average cost of Duval's algorithm for generating Lyndon words
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/0304-3975(94)00013-1
– ident: 10.1006/jagm.2000.1108_RF19
– volume: 29
  start-page: 671
  year: 1999
  ident: 10.1006/jagm.2000.1108_RF21
  article-title: An efficient algorithm for generating necklaces with fixed density
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539798344112
– year: 1983
  ident: 10.1006/jagm.2000.1108_RF16
– year: 1967
  ident: 10.1006/jagm.2000.1108_RF10
– year: 1989
  ident: 10.1006/jagm.2000.1108_RF15
– volume: 606
  year: 1992
  ident: 10.1006/jagm.2000.1108_RF13
– volume: 5
  start-page: 657
  year: 1961
  ident: 10.1006/jagm.2000.1108_RF8
  article-title: Symmetry types of periodic sequences
  publication-title: Illinois J. Math.
  doi: 10.1215/ijm/1255631587
– year: 1989
  ident: 10.1006/jagm.2000.1108_RF11
– year: 1994
  ident: 10.1006/jagm.2000.1108_RF14
– volume: 13
  start-page: 414
  year: 1992
  ident: 10.1006/jagm.2000.1108_RF20
  article-title: Generating necklaces
  publication-title: J. Algorithms
  doi: 10.1016/0196-6774(92)90047-G
– volume: 31
  start-page: 283
  year: 1988
  ident: 10.1006/jagm.2000.1108_RF4
  article-title: A fast algorithm for generating set partitions
  publication-title: Comput. J.
  doi: 10.1093/comjnl/31.3.283
– volume: 61
  start-page: 181
  year: 1986
  ident: 10.1006/jagm.2000.1108_RF5
  article-title: An algorithm for generating necklaces of beads in two colors
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(86)90089-0
– year: 1996
  ident: 10.1006/jagm.2000.1108_RF24
  article-title: Arithmetic and factorization of polynomials over F2
– volume: 60
  start-page: 255
  year: 1988
  ident: 10.1006/jagm.2000.1108_RF3
  article-title: Génération d'une section des classes de conjugaison et arbre des mots de Lyndon de longueur bornée
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/0304-3975(88)90113-2
– volume: 4
  start-page: 363
  year: 1983
  ident: 10.1006/jagm.2000.1108_RF2
  article-title: Factoring words over an ordered alphabet
  publication-title: J. Algorithms
  doi: 10.1016/0196-6774(83)90017-2
– year: 1993
  ident: 10.1006/jagm.2000.1108_RF18
SSID ssj0011549
Score 1.7059844
Snippet Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an...
SourceID pascalfrancis
crossref
elsevier
SourceType Index Database
Enrichment Source
Publisher
StartPage 267
SubjectTerms Exact sciences and technology
Group theory
Group theory and generalizations
Mathematics
Sciences and techniques of general use
Title Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
URI https://dx.doi.org/10.1006/jagm.2000.1108
Volume 37
WOSCitedRecordID wos000165183500003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1090-2678
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0011549
  issn: 0196-6774
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1db9MwFLVKxwMS4hsxGMgPSIBGhuMmjvNYoXWA0DSJDfUtsmNnVAtJ1WZl_Bl-K9dx4iSaKgESL1FluYnle3J97dx7DkIvIcaP4zDzPc6YhA2KCDxJZOZpFioacaVJnUTz9XN0fMzn8_hkNPrV1sJs8qgo-NVVvPyvpoY2MLYpnf0Lc7ubQgP8BqPDFcwO1z8y_Eysq_1pfl7Ctv_b95rAwXJLVyabMb2ok7DMzJ4VgABYddSwuU4QXq0MpevClFWdlPlPU7tc8yzDbOwfzSAqpe0RwvXAVrhndx84qsrVAW0WXfHZ5frCHpnX2vHutEf8EMrm8JYOd-DUakkkk-gvdC4GxxWkqdtzZ2htHc0gzdOQ9Hgssno9B9q6YhITjzIr8NP6aksQ02CS9h2vFfVo1nBqBY2uLQ_gYmpZgvOag8DWQHQLoUtP_GLGY4YDAajpwm-gHRqFMR-jnenHw_kn953KENzZgnw7_pYWlLB3w6dsC3tuL8UaXsbMqqj0QpvTe-hOYzo8tVi6j0a6eIDutnofuHH_D5E00MIdtHBV4hZa2GHoLXbA6jcCrHAPVrgHK2xghY9mr-mbR-hsdnj6_oPXaHR46YSTyouEENJnkZaZCrVU2tehnAgiBNdhlqkgELHiyg9ZNAmNTlUa-7ESGrbpGeMqmjxG46Is9BOEfeqnWeSnkikeBFIKEgQppb6KWZZxonaR105hkjYE9kZHJU8s9TZLzJQbXVWzryV8F71y_ZeWumVrT7-1SNIEnjagTAA4W_-zNzCdewQnYUj503-45TN0q3tj9tC4Wl3q5-hmuqkW69WLBnq_ARHir5U
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fast+Algorithms+to+Generate+Necklaces%2C+Unlabeled+Necklaces%2C+and+Irreducible+Polynomials+over+GF%282%29&rft.jtitle=Journal+of+algorithms&rft.au=Cattell%2C+Kevin&rft.au=Ruskey%2C+Frank&rft.au=Sawada%2C+Joe&rft.au=Serra%2C+Micaela&rft.date=2000-11-01&rft.pub=Elsevier+Inc&rft.issn=0196-6774&rft.eissn=1090-2678&rft.volume=37&rft.issue=2&rft.spage=267&rft.epage=282&rft_id=info:doi/10.1006%2Fjagm.2000.1108&rft.externalDocID=S0196677400911088
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0196-6774&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0196-6774&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0196-6774&client=summon