Categories of two-colored pair partitions part I: categories indexed by cyclic groups
We classify certain categories of partitions of finite sets subject to specific rules on the coloring of points and the sizes of blocks. More precisely, we consider pair partitions such that each block contains exactly one white and one black point when rotated to one line; however, crossings are al...
Uložené v:
| Vydané v: | The Ramanujan journal Ročník 53; číslo 1; s. 181 - 208 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.10.2020
Springer Nature B.V |
| Predmet: | |
| ISSN: | 1382-4090, 1572-9303 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We classify certain categories of partitions of finite sets subject to specific rules on the coloring of points and the sizes of blocks. More precisely, we consider pair partitions such that each block contains exactly one white and one black point when rotated to one line; however, crossings are allowed. There are two families of such categories, the first of which is indexed by cyclic groups and is covered in the present article; the second family will be the content of a follow-up article. Via a Tannaka–Krein result, the categories in the two families correspond to easy quantum groups interpolating the classical unitary group
U
n
and Wang’s free unitary quantum group
U
n
+
. In fact, they are all half-liberated in some sense and our results imply that there are many more half-liberation procedures than previously expected. However, we focus on a purely combinatorial approach leaving quantum group aspects aside. |
|---|---|
| AbstractList | We classify certain categories of partitions of finite sets subject to specific rules on the coloring of points and the sizes of blocks. More precisely, we consider pair partitions such that each block contains exactly one white and one black point when rotated to one line; however, crossings are allowed. There are two families of such categories, the first of which is indexed by cyclic groups and is covered in the present article; the second family will be the content of a follow-up article. Via a Tannaka–Krein result, the categories in the two families correspond to easy quantum groups interpolating the classical unitary group
U
n
and Wang’s free unitary quantum group
U
n
+
. In fact, they are all half-liberated in some sense and our results imply that there are many more half-liberation procedures than previously expected. However, we focus on a purely combinatorial approach leaving quantum group aspects aside. We classify certain categories of partitions of finite sets subject to specific rules on the coloring of points and the sizes of blocks. More precisely, we consider pair partitions such that each block contains exactly one white and one black point when rotated to one line; however, crossings are allowed. There are two families of such categories, the first of which is indexed by cyclic groups and is covered in the present article; the second family will be the content of a follow-up article. Via a Tannaka–Krein result, the categories in the two families correspond to easy quantum groups interpolating the classical unitary group Un and Wang’s free unitary quantum group Un+. In fact, they are all half-liberated in some sense and our results imply that there are many more half-liberation procedures than previously expected. However, we focus on a purely combinatorial approach leaving quantum group aspects aside. |
| Author | Mang, Alexander Weber, Moritz |
| Author_xml | – sequence: 1 givenname: Alexander orcidid: 0000-0003-4656-236X surname: Mang fullname: Mang, Alexander email: s9almang@stud.uni-saarland.de organization: Saarland University, Fachbereich Mathematik – sequence: 2 givenname: Moritz surname: Weber fullname: Weber, Moritz organization: Saarland University, Fachbereich Mathematik |
| BookMark | eNp9kMtKAzEUhoMo2FZfwNWA62iSk04y7qR4KRTc2HWYZDIlZZyMSUrt25u2QsFFF-ey-L9z-cfosve9ReiOkgdKiHiMlFKoMKE5COUV3l6gEZ0KhisgcJl7kAxzUpFrNI5xTQjhBMQILWd1sisfnI2Fb4u09dj4zgfbFEPtQk4hueR8Hw9tMX8qzIlwfWN_slTvCrMznTPFKvjNEG_QVVt30d7-1Qlavr58zt7x4uNtPnteYAO0SrjRoEFMQWrOpi2ztGwAhKCMNK2wmgmjdQmylLSWXBrQjRYWWgGUlS3THCbo_jh3CP57Y2NSa78JfV6pGOf5fwKVzCp5VJngYwy2Vcalev9UCrXrFCVqb6I6mqiyiepgotpmlP1Dh-C-6rA7D8ERilncr2w4XXWG-gUrFYc8 |
| CitedBy_id | crossref_primary_10_1016_j_jcta_2021_105409 crossref_primary_10_1007_s10485_021_09641_1 crossref_primary_10_1007_s10801_020_00998_5 |
| Cites_doi | 10.1007/BF02101540 10.1016/j.aim.2009.06.009 10.1007/s12044-017-0362-3 10.1112/jlms.12020 10.4171/JNCG/161 10.1007/BF01219077 10.1016/j.jcta.2017.09.003 10.1007/s00220-011-1301-2 10.2140/pjm.2013.263.13 10.1017/CBO9780511735127 10.1007/BF01393687 10.1007/BF00414633 10.1515/crelle-2014-0049 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2019 Springer Science+Business Media, LLC, part of Springer Nature 2019. |
| Copyright_xml | – notice: Springer Science+Business Media, LLC, part of Springer Nature 2019 – notice: Springer Science+Business Media, LLC, part of Springer Nature 2019. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11139-019-00149-w |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1572-9303 |
| EndPage | 208 |
| ExternalDocumentID | 10_1007_s11139_019_00149_w |
| GrantInformation_xml | – fundername: European Research Council grantid: NCDFP funderid: http://dx.doi.org/10.13039/501100000781 – fundername: Deutsche Forschungsgemeinschaft grantid: Quantenautomorphismen von Graphen; SFB-TRR 195 funderid: http://dx.doi.org/10.13039/501100001659 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 1SB 203 29P 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 6TJ 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADQRH ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P9R PF0 PT4 PT5 QOS R89 R9I RIG RNI ROL RPX RSV RZC RZE RZK S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7U ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABJCF ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ M2P M7S PHGZM PHGZT PQGLB PTHSS |
| ID | FETCH-LOGICAL-c319t-db3b37538b425f2e16d3377120df7eb27cbb638681a848c3bdb7e3f73126f2b43 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 5 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000567917500011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1382-4090 |
| IngestDate | Thu Sep 25 00:55:21 EDT 2025 Sat Nov 29 03:20:57 EST 2025 Tue Nov 18 22:06:51 EST 2025 Fri Feb 21 02:33:27 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Quantum group Half-liberation Tensor category 20G42 (Secondary) Category of partitions 05A18 (Primary) Two-colored partition Unitary easy quantum group Partition of a set Unitary group |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-db3b37538b425f2e16d3377120df7eb27cbb638681a848c3bdb7e3f73126f2b43 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-4656-236X |
| PQID | 2441570398 |
| PQPubID | 2043831 |
| PageCount | 28 |
| ParticipantIDs | proquest_journals_2441570398 crossref_citationtrail_10_1007_s11139_019_00149_w crossref_primary_10_1007_s11139_019_00149_w springer_journals_10_1007_s11139_019_00149_w |
| PublicationCentury | 2000 |
| PublicationDate | 2020-10-01 |
| PublicationDateYYYYMMDD | 2020-10-01 |
| PublicationDate_xml | – month: 10 year: 2020 text: 2020-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Dordrecht |
| PublicationSubtitle | An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan |
| PublicationTitle | The Ramanujan journal |
| PublicationTitleAbbrev | Ramanujan J |
| PublicationYear | 2020 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Bhowmick, D’Andrea, Das, Dabrowski (CR5) 2014; 8 Tarrago, Weber (CR11) 2017; 154 Freslon, Weber (CR7) 2016; 720 CR8 CR19 Tarrago, Weber (CR12) 2017; 2017 Bhowmick, D’Andrea, Dabrowski (CR4) 2011; 307 Woronowicz (CR18) 1991; 21 Bichon, Dubois-Violette (CR6) 2013; 263 Nica, Speicher (CR9) 2006 Wang (CR13) 1995; 167 Woronowicz (CR16) 1987; 111 Stanley (CR10) 2012 Banica, Bichon (CR1) 2016; 95 Woronowicz (CR17) 1987; 93 Banica, Speicher (CR3) 2009; 222 Weber (CR15) 2017; 127 Weber, Voiculescu, Stammeier, Weber (CR14) 2016 Banica, Bichon (CR2) 2017; 10 RP Stanley (149_CR10) 2012 T Banica (149_CR2) 2017; 10 J Bhowmick (149_CR5) 2014; 8 P Tarrago (149_CR12) 2017; 2017 SL Woronowicz (149_CR17) 1987; 93 S Wang (149_CR13) 1995; 167 M Weber (149_CR15) 2017; 127 J Bichon (149_CR6) 2013; 263 J Bhowmick (149_CR4) 2011; 307 SL Woronowicz (149_CR18) 1991; 21 SL Woronowicz (149_CR16) 1987; 111 A Nica (149_CR9) 2006 P Tarrago (149_CR11) 2017; 154 M Weber (149_CR14) 2016 T Banica (149_CR3) 2009; 222 A Freslon (149_CR7) 2016; 720 149_CR8 149_CR19 T Banica (149_CR1) 2016; 95 |
| References_xml | – ident: CR19 – volume: 720 start-page: 155 year: 2016 end-page: 199 ident: CR7 article-title: On the representation theory of easy quantum groups publication-title: J. für die reine und angewandte Mathematik – volume: 167 start-page: 671 issue: 3 year: 1995 end-page: 692 ident: CR13 article-title: Free products of compact quantum groups publication-title: Commun. Math. Phys. doi: 10.1007/BF02101540 – volume: 222 start-page: 1461 issue: 4 year: 2009 end-page: 1501 ident: CR3 article-title: Liberation of orthogonal Lie groups publication-title: Adv. Math. doi: 10.1016/j.aim.2009.06.009 – volume: 127 start-page: 881 year: 2017 end-page: 933 ident: CR15 article-title: Introduction to compact (matrix) quantum groups and Banica–Speicher (easy) quantum groups publication-title: Proc. Indian Acad. Sci. Math. Sci. doi: 10.1007/s12044-017-0362-3 – volume: 95 start-page: 519 issue: 2 year: 2016 end-page: 540 ident: CR1 article-title: Matrix models for noncommutative algebraic manifolds publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms.12020 – volume: 8 start-page: 433 year: 2014 end-page: 471 ident: CR5 article-title: Quantum gauge symmetries in noncommutative geometry publication-title: J. Noncommutat. Geom. doi: 10.4171/JNCG/161 – year: 2012 ident: CR10 publication-title: Enumerative Combinatorics – year: 2016 ident: CR14 article-title: Easy quantum groups publication-title: Free Probability and Operator Algebras – volume: 2017 start-page: 5710 issue: 18 year: 2017 end-page: 5750 ident: CR12 article-title: Unitary easy quantum groups: the free case and the group case publication-title: Int. Math. Res. Not. – volume: 111 start-page: 613 issue: 4 year: 1987 end-page: 665 ident: CR16 article-title: Compact matrix pseudogroups publication-title: Commun. Math. Phys. doi: 10.1007/BF01219077 – volume: 154 start-page: 464 year: 2017 end-page: 506 ident: CR11 article-title: The classification of tensor categories of two-colored noncrossing partitions publication-title: J. Comb. Theory A doi: 10.1016/j.jcta.2017.09.003 – volume: 307 start-page: 101 year: 2011 end-page: 131 ident: CR4 article-title: Quantum Isometries of the finite noncommutative geometry of the standard model publication-title: Commun. Math. Phys. doi: 10.1007/s00220-011-1301-2 – volume: 263 start-page: 13 issue: 1 year: 2013 end-page: 28 ident: CR6 article-title: Half-commutative orthogonal hopf algebras publication-title: Pac. J. Math. doi: 10.2140/pjm.2013.263.13 – ident: CR8 – year: 2006 ident: CR9 publication-title: Lectures on the Combinatorics of Free Probability doi: 10.1017/CBO9780511735127 – volume: 10 start-page: 457 year: 2017 end-page: 483 ident: CR2 article-title: Complex analogues of the half-classical geometry publication-title: Münster J. Math. – volume: 93 start-page: 35 issue: 1 year: 1987 end-page: 76 ident: CR17 article-title: Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups publication-title: Invent. Math. doi: 10.1007/BF01393687 – volume: 21 start-page: 35 issue: 1 year: 1991 end-page: 39 ident: CR18 article-title: A remark on compact matrix quantum groups publication-title: Lett. Math. Phys. doi: 10.1007/BF00414633 – volume: 167 start-page: 671 issue: 3 year: 1995 ident: 149_CR13 publication-title: Commun. Math. Phys. doi: 10.1007/BF02101540 – volume: 127 start-page: 881 year: 2017 ident: 149_CR15 publication-title: Proc. Indian Acad. Sci. Math. Sci. doi: 10.1007/s12044-017-0362-3 – volume: 21 start-page: 35 issue: 1 year: 1991 ident: 149_CR18 publication-title: Lett. Math. Phys. doi: 10.1007/BF00414633 – volume: 263 start-page: 13 issue: 1 year: 2013 ident: 149_CR6 publication-title: Pac. J. Math. doi: 10.2140/pjm.2013.263.13 – volume: 720 start-page: 155 year: 2016 ident: 149_CR7 publication-title: J. für die reine und angewandte Mathematik doi: 10.1515/crelle-2014-0049 – volume: 10 start-page: 457 year: 2017 ident: 149_CR2 publication-title: Münster J. Math. – volume: 307 start-page: 101 year: 2011 ident: 149_CR4 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-011-1301-2 – ident: 149_CR8 – volume-title: Enumerative Combinatorics year: 2012 ident: 149_CR10 – volume: 154 start-page: 464 year: 2017 ident: 149_CR11 publication-title: J. Comb. Theory A doi: 10.1016/j.jcta.2017.09.003 – volume: 111 start-page: 613 issue: 4 year: 1987 ident: 149_CR16 publication-title: Commun. Math. Phys. doi: 10.1007/BF01219077 – volume: 2017 start-page: 5710 issue: 18 year: 2017 ident: 149_CR12 publication-title: Int. Math. Res. Not. – ident: 149_CR19 – volume: 93 start-page: 35 issue: 1 year: 1987 ident: 149_CR17 publication-title: Invent. Math. doi: 10.1007/BF01393687 – volume: 222 start-page: 1461 issue: 4 year: 2009 ident: 149_CR3 publication-title: Adv. Math. doi: 10.1016/j.aim.2009.06.009 – volume-title: Free Probability and Operator Algebras year: 2016 ident: 149_CR14 – volume-title: Lectures on the Combinatorics of Free Probability year: 2006 ident: 149_CR9 doi: 10.1017/CBO9780511735127 – volume: 95 start-page: 519 issue: 2 year: 2016 ident: 149_CR1 publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms.12020 – volume: 8 start-page: 433 year: 2014 ident: 149_CR5 publication-title: J. Noncommutat. Geom. doi: 10.4171/JNCG/161 |
| SSID | ssj0004037 |
| Score | 2.251183 |
| Snippet | We classify certain categories of partitions of finite sets subject to specific rules on the coloring of points and the sizes of blocks. More precisely, we... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 181 |
| SubjectTerms | Categories Combinatorial analysis Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory Partitions (mathematics) |
| Title | Categories of two-colored pair partitions part I: categories indexed by cyclic groups |
| URI | https://link.springer.com/article/10.1007/s11139-019-00149-w https://www.proquest.com/docview/2441570398 |
| Volume | 53 |
| WOSCitedRecordID | wos000567917500011&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: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1572-9303 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: RSV dateStart: 19970301 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/eLvHCXMwnV3fS8MwED50-qAP_hanU_LgmwbaZmtS32Q49MEh6mRvpUkbGMg62urYf-8lbVcUFfShpdBLCJdc7j6S-w7gnKOLc5I4prosYeYpKrXyqSEmUVFgSL_LYhN8OBTjcfBQJYXl9W33-kjS7tRNspuL0QpCX3xMXE_nq7CG7k4Yc3x8emmyIR3LlGnI9RAdBU6VKvN9H5_dURNjfjkWtd5msP2_ce7AVhVdkutyOezCSjLdg837JTVrvg-jvuGGSA1CJqkmxTylhrg6S2IyiyYZvrKSvyi3n-TuiqimhSVXRFG5IGqhXieK2LSQ_ABGg5vn_i2taitQhUZX0FgyyRCqCIlGq73E9WPGOHc9J9Yc0TZXUqJp-sKNRFcoJg0NM9OcuZ6vPdllh9CaptPkCIgUPc05wiAlAwz_VMCCyI997fAYt9oea4NbqzhUFfG4qX_xGjaUyUZlIaostCoL5224WLaZlbQbv0p36pkLKxPMQ88gRdzPAtGGy3qmmt8_93b8N_ET2PAMBrcX_DrQKrK35BTW1XsxybMzuzQ_ACI53OM |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fS8MwED50CuqDv8Xp1Dz4poW22ZrWNxmODbchusneypI2MBjraKtj_72XtF1RVNCHlkKTEC653H3k7juAa4YmzgyDwJBZCTNbGFwKx1DEJGLsKdLvrNgE6_fd0ch7ypPCkiLavbiS1Cd1mexmobeC0Bcf5dcbi3XYqKPFUoF8zy-vZTakqZkyFbkeoiPPzFNlvh_jszkqfcwv16La2rT2_jfPfdjNvUtyn22HA1gLZ4ew01tRsyZHMGwqbohIIWQSSZIuIkMRV8dhQObjSYyvOOMvSvQn6dwRUfbQ5IrYlC-JWIrpRBCdFpIcw7D1MGi2jby2giFQ6VIj4JRThCouR6WVdmg5AaWMWbYZSIZomwnOUTUd1xq7dVdQrmiYqWTUsh1p8zo9gcosmoWnQLjbkIwhDBLcQ_dPeNQbO4EjTRbgUdugVbAKEfsiJx5X9S-mfkmZrETmo8h8LTJ_UYWbVZ95Rrvxa-tasXJ-roKJbyukiOeZ51bhtlip8vfPo539rfkVbLUHva7f7fQfz2HbVnhcB_vVoJLGb-EFbIr3dJLEl3qbfgCF_t_H |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpZ3fS8MwEMcPnSL64G9xOjUPvmlZ22xN65tMh0MdA53srSxJA4OxjbY69t97SbtVRQXxoaXQpJTLr_uS3OcAzhkucXYkpaWyFGausLgSnqXBJKIfaOh3lmyCtdt-rxd0PkTxm9Pu8y3JLKZBU5pGaXUiVbUIfHPQc0EZjJf28a3pMqzUdNIgrdefXorISNtQMzVoD5VSYOdhM99_4_PSVPibX7ZIzcrT3Pr_P2_DZu51kuusm-zAUjTahY3HBbI12YNuQzMjxlo5k7Ei6XRsaaB1HEky6Q9ivMUZ1ygxj6R1RURRw0AXsSifETETw4EgJlwk2Ydu8_a5cWflORcsgYMxtSSnnKKE8TkOZuVGjicpZcxxbakYqnAmOMch6_lO36_5gnKNZ6aKUcf1lMtr9ABKo_EoOgTC_bpiDOWR4AG6hSKgQd-TnrKZxCm4TsvgzM0dihxIrvNiDMMCpaxNFqLJQmOycFqGi0WdSYbj-LV0Zd6KYT40k9DVChLnucAvw-W81YrXP3_t6G_Fz2Ctc9MMH1rt-2NYd7VMN2cAK1BK49foBFbFWzpI4lPTY98B7qDoqw |
| 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=Categories+of+two-colored+pair+partitions+part+I%3A+categories+indexed+by+cyclic+groups&rft.jtitle=The+Ramanujan+journal&rft.au=Mang%2C+Alexander&rft.au=Weber%2C+Moritz&rft.date=2020-10-01&rft.pub=Springer+US&rft.issn=1382-4090&rft.eissn=1572-9303&rft.volume=53&rft.issue=1&rft.spage=181&rft.epage=208&rft_id=info:doi/10.1007%2Fs11139-019-00149-w&rft.externalDocID=10_1007_s11139_019_00149_w |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1382-4090&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1382-4090&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1382-4090&client=summon |