On the Joint Distributions of Increasing and Decreasing Successions of Arbitrary Multisets

The joint distribution of increasing and decreasing successions in arbitrary multisets has remained an open problem for a long time. Here, we present a systematic approach inspired by methods in statistical physics to solve this problem. Using the two-step approach to pattern distributions in random...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Methodology and computing in applied probability Ročník 27; číslo 3; s. 57
Hlavný autor: Kong, Yong
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.09.2025
Springer Nature B.V
Predmet:
Business and Management
Economics
Electrical Engineering
Life Sciences
Mathematics and Statistics
Statistical methods
Statistics
60C05
Random permutations of multisets
68R05
Generating functions
68R15
Combinatorial probability
Exact enumeration problems
System of recurrences
Increasing and decreasing successions
Increasing and decreasing 2-sequences
05A05
05A15
62E15
ISSN:1387-5841, 1573-7713
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract The joint distribution of increasing and decreasing successions in arbitrary multisets has remained an open problem for a long time. Here, we present a systematic approach inspired by methods in statistical physics to solve this problem. Using the two-step approach to pattern distributions in random sequences previously developed by the author, we derive recurrence and explicit formulas for the generating functions of increasing and decreasing successions in multisets. From these generating functions, explicit formulas for the mean, variance, and covariance are obtained.
AbstractList The joint distribution of increasing and decreasing successions in arbitrary multisets has remained an open problem for a long time. Here, we present a systematic approach inspired by methods in statistical physics to solve this problem. Using the two-step approach to pattern distributions in random sequences previously developed by the author, we derive recurrence and explicit formulas for the generating functions of increasing and decreasing successions in multisets. From these generating functions, explicit formulas for the mean, variance, and covariance are obtained.
ArticleNumber 57
Author Kong, Yong
Author_xml – sequence: 1
  givenname: Yong
  surname: Kong
  fullname: Kong, Yong
  email: yong.kong@yale.edu
  organization: Department of Biostatistics, School of Public Health, Yale University
BookMark eNp9kDtPAzEQhC0UJELgD1BZojas7dz5rowSHkFBKYCGxrLv7OAo-ILtK_j3GI5HRzW70jezqzlGI995g9AZhQsKIC4jzVITYAWhQKuSsAM0poXgRAjKR3nmlSBFNaVH6DjGLQCjBZ-O0fPa4_Ri8F3nfMILF1Nwuk-u8xF3Fi99E4yKzm-w8i1emN_1oW8aE-MPOAvapaDCO77vd8lFk-IJOrRqF83pt07Q0_XV4_yWrNY3y_lsRRomWCKaU7CiBq2VbitmtYVW1WAaVRZgmCot01QYVnFoS8HNVEFdVJq3NWNNaQ2foPMhdx-6t97EJLddH3w-KTljJbCyrqeZYgPVhC7GYKzcB_eaH5YU5GeHcuhQ5g7lV4eSZRMfTDHDfmPCX_Q_rg-e0HcB
Cites_doi 10.1017/CBO9780511801655
10.1007/978-1-4614-8414-1_56-1
10.1103/PhysRevE.74.061102
10.1080/01621459.1994.10476841
10.1080/00029890.1980.11994973
10.1007/s11009-018-9689-1
10.1198/016214505000001401
10.1214/aoms/1177731121
10.1080/03610926.2017.1414261
10.1080/03610926.2020.1767137
10.1017/CBO9781139058520
10.1016/S0167-7152(02)00195-5
10.1007/978-94-010-2196-8
10.1007/BF01856545
10.1016/j.cam.2021.113846
10.1214/aoms/1177700181
10.1016/S0301-4622(96)02178-3
10.1142/9789812779205
ContentType Journal Article
Copyright The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Copyright_xml – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
– notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
DBID AAYXX
CITATION
JQ2
DOI 10.1007/s11009-025-10186-2
DatabaseName CrossRef
ProQuest Computer Science Collection
DatabaseTitle CrossRef
ProQuest Computer Science Collection
DatabaseTitleList ProQuest Computer Science Collection
DeliveryMethod fulltext_linktorsrc
Discipline Economics
Statistics
Mathematics
EISSN 1573-7713
ExternalDocumentID 10_1007_s11009_025_10186_2
GroupedDBID -~C
.86
.VR
06D
0R~
0VY
123
1N0
203
29M
2J2
2JN
2JY
2KG
2LR
2~H
30V
4.4
406
408
409
40D
40E
5VS
67Z
6NX
7WY
8FL
8TC
8UJ
8VB
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AAPKM
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
ABAKF
ABBBX
ABBRH
ABBXA
ABDBE
ABDZT
ABECU
ABFSG
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABRTQ
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABWNU
ABXPI
ACAOD
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACSTC
ACZOJ
ADHHG
ADHIR
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEMSY
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AEZWR
AFBBN
AFDZB
AFHIU
AFLOW
AFOHR
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHPBZ
AHWEU
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AIXLP
AJRNO
AJZVZ
AKVCP
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARMRJ
ASPBG
ATHPR
AVWKF
AXYYD
AYFIA
AYJHY
AZFZN
B-.
BA0
BAPOH
BENPR
BGNMA
BSONS
CS3
CSCUP
DDRTE
DL5
DNIVK
DPUIP
DU5
EBLON
EBS
EBU
EIOEI
ESBYG
F5P
FEDTE
FERAY
FFXSO
FIGPU
FNLPD
FRRFC
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ7
GQ8
GXS
HCIFZ
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
I09
IJ-
IKXTQ
IWAJR
IXC
IXD
IXE
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
J9A
JBSCW
JCJTX
JZLTJ
K60
K6~
KDC
KOV
LAK
LLZTM
M4Y
MA-
NB0
NPVJJ
NQJWS
NU0
O93
O9J
OAM
P2P
P9R
PF0
PT4
PT5
QOS
QWB
R89
R9I
ROL
RPX
RSV
S16
S1Z
S27
S3B
SAP
SDH
SHX
SISQX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
TSG
TSK
TSV
TUC
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
YLTOR
Z45
ZL0
ZMTXR
-Y2
1SB
2P1
2VQ
88I
8AO
8FE
8FG
8FW
AARHV
AAYXX
ABJCF
ABQSL
ABULA
ABUWG
ACBXY
ADHKG
AEBTG
AEKMD
AFFHD
AFGCZ
AFKRA
AGGDS
AGQPQ
AHQJS
AHSBF
AJBLW
AMVHM
AZQEC
BDATZ
BEZIV
BGLVJ
BPHCQ
CAG
CCPQU
CITATION
COF
DWQXO
EBO
EJD
FINBP
FRNLG
FSGXE
GNUQQ
GROUPED_ABI_INFORM_RESEARCH
H13
HZ~
IHE
K1G
K6V
K7-
L6V
M0C
M2P
M7S
N2Q
O9-
OVD
P62
PHGZM
PHGZT
PQBIZ
PQBZA
PQGLB
PQQKQ
PROAC
PTHSS
Q2X
RNI
RZC
RZE
RZK
TEORI
TH9
~8M
JQ2
ID FETCH-LOGICAL-c272t-b310f790bbabd82fbf0da90eca650e2a6f2b17e2830d673e4a0958b3d922c6fe3
IEDL.DBID RSV
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001520783800002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1387-5841
IngestDate Wed Nov 05 08:49:23 EST 2025
Sat Nov 29 07:15:58 EST 2025
Tue Oct 14 01:10:51 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 3
Keywords 60C05
Random permutations of multisets
68R05
Generating functions
68R15
Combinatorial probability
Exact enumeration problems
System of recurrences
Increasing and decreasing successions
Increasing and decreasing 2-sequences
05A05
05A15
62E15
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c272t-b310f790bbabd82fbf0da90eca650e2a6f2b17e2830d673e4a0958b3d922c6fe3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 3226026994
PQPubID 26119
ParticipantIDs proquest_journals_3226026994
crossref_primary_10_1007_s11009_025_10186_2
springer_journals_10_1007_s11009_025_10186_2
PublicationCentury 2000
PublicationDate 2025-09-01
PublicationDateYYYYMMDD 2025-09-01
PublicationDate_xml – month: 09
  year: 2025
  text: 2025-09-01
  day: 01
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle Methodology and computing in applied probability
PublicationTitleAbbrev Methodol Comput Appl Probab
PublicationYear 2025
Publisher Springer US
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer Nature B.V
References 10186_CR5
Y Kong (10186_CR15) 2020; 51
BC Johnson (10186_CR7) 2002; 59
Y Kong (10186_CR18) 2024
10186_CR23
Y Kong (10186_CR17) 2022; 403
10186_CR10
J Riordan (10186_CR21) 1965; 36
P Flajolet (10186_CR6) 2009
Y Kong (10186_CR13) 2019; 21
PA MacMahon (10186_CR19) 1915
N Balakrishnan (10186_CR1) 2002
Y Kong (10186_CR14) 2019; 48
L Comtet (10186_CR2) 1974
MV Koutras (10186_CR8) 1995; 47
J Riordan (10186_CR20) 1958
DP Robbins (10186_CR22) 1980; 87
10186_CR16
10186_CR24
E Di Cera (10186_CR3) 1996; 61
I Kaplansky (10186_CR9) 1945; 16
Y Kong (10186_CR12) 2006; 101
Y Kong (10186_CR11) 2006; 74
JC Fu (10186_CR4) 1994; 89
References_xml – volume-title: Runs and Scans with Applications
  year: 2002
  ident: 10186_CR1
– start-page: 1
  volume-title: Handbook of Scan Statistics
  year: 2024
  ident: 10186_CR18
– volume-title: Analytic Combinatorics
  year: 2009
  ident: 10186_CR6
  doi: 10.1017/CBO9780511801655
– volume-title: Combinatory Analysis
  year: 1915
  ident: 10186_CR19
– ident: 10186_CR16
  doi: 10.1007/978-1-4614-8414-1_56-1
– volume: 74
  start-page: 061102
  issue: 6
  year: 2006
  ident: 10186_CR11
  publication-title: Phys Rev E
  doi: 10.1103/PhysRevE.74.061102
– volume: 89
  start-page: 1050
  year: 1994
  ident: 10186_CR4
  publication-title: J Am Stat Assoc
  doi: 10.1080/01621459.1994.10476841
– volume: 87
  start-page: 122
  year: 1980
  ident: 10186_CR22
  publication-title: Am Math Mon
  doi: 10.1080/00029890.1980.11994973
– volume: 21
  start-page: 789
  year: 2019
  ident: 10186_CR13
  publication-title: Methodol Comput Appl Probab
  doi: 10.1007/s11009-018-9689-1
– volume: 101
  start-page: 1253
  year: 2006
  ident: 10186_CR12
  publication-title: J Am Stat Assoc
  doi: 10.1198/016214505000001401
– ident: 10186_CR23
– volume: 16
  start-page: 200
  year: 1945
  ident: 10186_CR9
  publication-title: Ann Math Statist
  doi: 10.1214/aoms/1177731121
– volume: 48
  start-page: 493
  issue: 3
  year: 2019
  ident: 10186_CR14
  publication-title: Commun Stat - Theory Meth
  doi: 10.1080/03610926.2017.1414261
– volume: 51
  start-page: 1693
  issue: 6
  year: 2020
  ident: 10186_CR15
  publication-title: Commun Stat-Theory Meth
  doi: 10.1080/03610926.2020.1767137
– ident: 10186_CR24
  doi: 10.1017/CBO9781139058520
– volume: 59
  start-page: 67
  issue: 1
  year: 2002
  ident: 10186_CR7
  publication-title: Stat Probab Lett
  doi: 10.1016/S0167-7152(02)00195-5
– volume-title: An Introduction to Combinatorial Analysis
  year: 1958
  ident: 10186_CR20
– volume-title: Advanced Combinatorics: The Art of Finite and Infinite Expansions
  year: 1974
  ident: 10186_CR2
  doi: 10.1007/978-94-010-2196-8
– volume: 47
  start-page: 743
  issue: 4
  year: 1995
  ident: 10186_CR8
  publication-title: Ann Inst Stat Math
  doi: 10.1007/BF01856545
– volume: 403
  start-page: 113846
  year: 2022
  ident: 10186_CR17
  publication-title: J Comput Appl Math
  doi: 10.1016/j.cam.2021.113846
– ident: 10186_CR10
– volume: 36
  start-page: 708
  issue: 2
  year: 1965
  ident: 10186_CR21
  publication-title: Ann Math Stat
  doi: 10.1214/aoms/1177700181
– volume: 61
  start-page: 107
  issue: 2
  year: 1996
  ident: 10186_CR3
  publication-title: Biophys Chem
  doi: 10.1016/S0301-4622(96)02178-3
– ident: 10186_CR5
  doi: 10.1142/9789812779205
SSID ssj0021534
Score 2.3505456
Snippet The joint distribution of increasing and decreasing successions in arbitrary multisets has remained an open problem for a long time. Here, we present a...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Index Database
Publisher
StartPage 57
SubjectTerms Business and Management
Economics
Electrical Engineering
Life Sciences
Mathematics and Statistics
Statistical methods
Statistics
Title On the Joint Distributions of Increasing and Decreasing Successions of Arbitrary Multisets
URI https://link.springer.com/article/10.1007/s11009-025-10186-2
https://www.proquest.com/docview/3226026994
Volume 27
WOSCitedRecordID wos001520783800002&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: PRVAVX
  databaseName: Springer Nature - Connect here FIRST to enable access
  customDbUrl:
  eissn: 1573-7713
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0021534
  issn: 1387-5841
  databaseCode: RSV
  dateStart: 19990701
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED9kCs4HP6bidEoefNNCm8W0eRzOIYJTnMrwpSRNCnvpZO38-72k7YqiD_oYEkK4u9z98nG_AzgXVNLUoPHiWUB5THHmqUAKL_W5tIBXJ0q6YhPheBxNp-KxSgrL69_u9ZOk89RNslvgLvKpZc4MIu6h413HcBfZ7fg0eV0ds3APl6VscQUYXoMqVebnOb6GowZjfnsWddFmtPO_de7CdoUuyaA0hz1YM1kHNuvk47wDW_crmlZstS3ULJma9-HtISPYR-7ms6wgQ0uoW9XCysk8JehI7P91XAmRmSZDs2pOlq7oYj1wsFAzl8tPXHJvbor8AF5GN8_Xt15VecFLaEgLTyHoS0PhKyWVjmiqUl9L4ZtEIqAzVPKUqiA0ljxM87BvmESkFqm-FpQmPDX9Q2hl88wcATGBUAmPeN_4jJkrKTWPpGQsxEk1DUwXLmoFxO8lwUbcUClbUcYoytiJMqZd6NU6iqvNlsfok2whLSFYFy5rnTTdv892_LfhJ9CmVq3uh1kPWsViaU5hI_lAWS7OnBF-AsbP1w0
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fT8IwEL4YNAEf_IEaUdQ--KZLtq526yMRDSqgETTEl6XduoSXYRj493stG0SjD_rYtGmau_bua3v3HcC5oJKmGjcv3gWUwxRnjvKkcFKXSwN4k1hJW2wi6PfD0Ug8FUlheRntXn5JWku9Snbz7EM-NcyZXsgdNLzrDD2WCeR7Hrwur1l4hhelbHEF6F69IlXm5zm-uqMVxvz2LWq9ze32_9a5A1sFuiStxXbYhTWd1aFaJh_nddjsLWlasVUzUHPB1LwHb48ZwT5yPxlnM9I2hLpFLaycTFKChsTEr-NKiMwS0tbL5mBuiy6WA1tTNba5_MQm9-Z6lu_Dy-3N8LrjFJUXnJgGdOYoBH1pIFylpEpCmqrUTaRwdSwR0GkqeUqVF2hDHpbwwNdMIlILlZ8ISmOeav8AKtkk04dAtCdUzEPua5cxfSVlwkMpGQtw0oR6ugEXpQKi9wXBRrSiUjaijFCUkRVlRBvQLHUUFYctj9AmmUJaQrAGXJY6WXX_PtvR34afQbUz7HWj7l3_4Rhq1KjYRps1oTKbzvUJbMQfKNfpqd2Qn-R02fE
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1JS8QwGP0QFZeDuziuOXjTYpuJaXMUx8F1FFwQLyVpEphLR6bV3--XtJ1R0YN4LAkhfF-WlybvPYB9QSW1BgcvngVUwBRngYqkCGzIpQO8OlPSm03EvV7y_CzuPrH4_Wv35kqy4jQ4laa8PHrV9mhMfIv8T33qVDSjhAe4CE8xZxrkzuv3T6MjF87nytYWe4NbbVTTZn5u4-vWNMab365I_c7TXfx_n5dgoUad5KQaJsswYfIVmG1IycUKzN-M5Fvxa85B0ErBeRVebnOCZeRy0M9L0nFCu7VHVkEGluAC4961Y6-IzDXpmNHn_Zs3Y2wqngxV33P8iSf9FqYs1uCxe_Zweh7UjgxBRmNaBgrBoI1FqJRUOqFW2VBLEZpMItAzVHJLVRQbJyqmedw2TCKCS1RbC0ozbk17HSbzQW42gJhIqIwnvG1CxsyxlJonUjIWY6OaRqYFB00y0tdKeCMdSyy7UKYYytSHMqUt2G7yldaTsEhxrXIGW0KwFhw2-RkX_97a5t-q78HMXaebXl_0rrZgjroM-0do2zBZDt_MDkxn7xjW4a4fmx-MBeLV
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=On+the+Joint+Distributions+of+Increasing+and+Decreasing+Successions+of+Arbitrary+Multisets&rft.jtitle=Methodology+and+computing+in+applied+probability&rft.au=Kong%2C+Yong&rft.date=2025-09-01&rft.pub=Springer+US&rft.issn=1387-5841&rft.eissn=1573-7713&rft.volume=27&rft.issue=3&rft_id=info:doi/10.1007%2Fs11009-025-10186-2&rft.externalDocID=10_1007_s11009_025_10186_2
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1387-5841&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1387-5841&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1387-5841&client=summon