Wang, Liuquan New proofs of some double sum Rogers-Ramanujan type identities. (English) Zbl 07739356 Ramanujan J. 62, No. 1, 251-272 (2023). MSC: 11P84 33D15 11B65 PDFBibTeX XMLCite \textit{L. Wang}, Ramanujan J. 62, No. 1, 251--272 (2023; Zbl 07739356) Full Text: DOI arXiv
McLaughlin, James Some more identities of Kanade-Russell type derived using Rosengren’s method. (English) Zbl 07711278 Ann. Comb. 27, No. 2, 329-352 (2023). MSC: 33D15 33D45 11P84 PDFBibTeX XMLCite \textit{J. McLaughlin}, Ann. Comb. 27, No. 2, 329--352 (2023; Zbl 07711278) Full Text: DOI
Rosengren, Hjalmar Proofs of some partition identities conjectured by Kanade and Russell. (English) Zbl 1523.11189 Ramanujan J. 61, No. 1, 295-317 (2023). Reviewer: Mircea Merca (Cornu de Jos) MSC: 11P84 33D15 33D45 PDFBibTeX XMLCite \textit{H. Rosengren}, Ramanujan J. 61, No. 1, 295--317 (2023; Zbl 1523.11189) Full Text: DOI arXiv
Dousse, Jehanne; Konan, Isaac Generalisations of Capparelli’s and Primc’s identities. I: Coloured Frobenius partitions and combinatorial proofs. (English) Zbl 1497.05010 Adv. Math. 408, Part B, Article ID 108571, 70 p. (2022). Reviewer: Mircea Merca (Cornu de Jos) MSC: 05A17 11P84 05A15 05A19 05E10 17B37 17B65 PDFBibTeX XMLCite \textit{J. Dousse} and \textit{I. Konan}, Adv. Math. 408, Part B, Article ID 108571, 70 p. (2022; Zbl 1497.05010) Full Text: DOI arXiv
Capparelli, S.; Del Fra, A.; Mercuri, P.; Vietri, A. Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection. (English) Zbl 1485.11150 Ramanujan J. 57, No. 1, 175-188 (2022). Reviewer: Mircea Merca (Cornu de Jos) MSC: 11P84 05A17 11P82 11P83 PDFBibTeX XMLCite \textit{S. Capparelli} et al., Ramanujan J. 57, No. 1, 175--188 (2022; Zbl 1485.11150) Full Text: DOI arXiv
Berkovich, Alexander; Uncu, Ali Kemal New infinite hierarchies of polynomial identities related to the Capparelli partition theorems. (English) Zbl 1475.05012 J. Math. Anal. Appl. 506, No. 2, Article ID 125678, 18 p. (2022). MSC: 05A17 11P81 05A19 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{A. K. Uncu}, J. Math. Anal. Appl. 506, No. 2, Article ID 125678, 18 p. (2022; Zbl 1475.05012) Full Text: DOI arXiv
Takigiku, Motoki; Tsuchioka, Shunsuke Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra \(A^{(2)}_2\). (English) Zbl 1475.11188 Proc. Am. Math. Soc. 149, No. 7, 2763-2776 (2021). MSC: 11P84 05E10 17B67 PDFBibTeX XMLCite \textit{M. Takigiku} and \textit{S. Tsuchioka}, Proc. Am. Math. Soc. 149, No. 7, 2763--2776 (2021; Zbl 1475.11188) Full Text: DOI arXiv
Berkovich, Alexander; Uncu, Ali Kemal Refined \(q\)-trinomial coefficients and two infinite hierarchies of \(q\)-series identities. (English) Zbl 07293158 Pillwein, Veronika (ed.) et al., Algorithmic combinatorics: enumerative combinatorics, special functions and computer algebra. Proceedings of the workshop on combinatorics, special functions and computer algebra (Paule60), Research Institute of Symbolic Computation (RISC), Hagenberg, Austria, May 17–18, 2018. In honour of Peter Paule on his 60th birthday. Cham: Springer. Texts Monogr. Symb. Comput., 47-61 (2020). MSC: 68W30 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{A. K. Uncu}, in: Algorithmic combinatorics: enumerative combinatorics, special functions and computer algebra. Proceedings of the workshop on combinatorics, special functions and computer algebra (Paule60), Research Institute of Symbolic Computation (RISC), Hagenberg, Austria, May 17--18, 2018. In honour of Peter Paule on his 60th birthday. Cham: Springer. 47--61 (2020; Zbl 07293158) Full Text: DOI arXiv
Bringmann, Kathrin; Jennings-Shaffer, Chris; Mahlburg, Karl Proofs and reductions of various conjectured partition identities of Kanade and Russell. (English) Zbl 1447.05023 J. Reine Angew. Math. 766, 109-135 (2020). MSC: 05A17 05A19 11P84 PDFBibTeX XMLCite \textit{K. Bringmann} et al., J. Reine Angew. Math. 766, 109--135 (2020; Zbl 1447.05023) Full Text: DOI arXiv
Dousse, Jehanne On partition identities of Capparelli and Primc. (English) Zbl 1442.05017 Adv. Math. 370, Article ID 107245, 21 p. (2020). MSC: 05A17 11P84 17B37 PDFBibTeX XMLCite \textit{J. Dousse}, Adv. Math. 370, Article ID 107245, 21 p. (2020; Zbl 1442.05017) Full Text: DOI arXiv
Uncu, Ali Kemal A polynomial identity implying Schur’s partition theorem. (English) Zbl 1441.05026 Proc. Am. Math. Soc. 148, No. 8, 3307-3324 (2020). MSC: 05A19 05A15 05A17 11B37 11P83 PDFBibTeX XMLCite \textit{A. K. Uncu}, Proc. Am. Math. Soc. 148, No. 8, 3307--3324 (2020; Zbl 1441.05026) Full Text: DOI arXiv
Dousse, Jehanne On partition identities of Capparelli and Primc. (English) Zbl 1436.05017 Sémin. Lothar. Comb. 82B, Article 53, 12 p. (2019). MSC: 05A17 05A19 05E10 17B67 PDFBibTeX XMLCite \textit{J. Dousse}, Sémin. Lothar. Comb. 82B, Article 53, 12 p. (2019; Zbl 1436.05017) Full Text: Link
Berkovich, Alexander; Uncu, Ali Kemal Elementary polynomial identities involving \(q\)-trinomial coefficients. (English) Zbl 1431.11030 Ann. Comb. 23, No. 3-4, 549-560 (2019). MSC: 11B65 11C08 11P81 11P82 11P83 11P84 05A10 05A15 05A17 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{A. K. Uncu}, Ann. Comb. 23, No. 3--4, 549--560 (2019; Zbl 1431.11030) Full Text: DOI arXiv
Gorodetsky, Ofir \(q\)-congruences, with applications to supercongruences and the cyclic sieving phenomenon. (English) Zbl 1423.11043 Int. J. Number Theory 15, No. 9, 1919-1968 (2019). MSC: 11B65 05A30 11A07 11B83 PDFBibTeX XMLCite \textit{O. Gorodetsky}, Int. J. Number Theory 15, No. 9, 1919--1968 (2019; Zbl 1423.11043) Full Text: DOI arXiv
Chen, Shi-Chao Parity of Schur’s partition function. (Parité de la fonction de partition de Schur.) (English. French summary) Zbl 1467.11090 C. R., Math., Acad. Sci. Paris 357, No. 5, 418-423 (2019). Reviewer: Mircea Merca (Cornu de Jos) MSC: 11P83 PDFBibTeX XMLCite \textit{S.-C. Chen}, C. R., Math., Acad. Sci. Paris 357, No. 5, 418--423 (2019; Zbl 1467.11090) Full Text: DOI
Dousse, Jehanne; Lovejoy, Jeremy Generalizations of Capparelli’s identity. (English) Zbl 1430.11144 Bull. Lond. Math. Soc. 51, No. 2, 193-206 (2019). Reviewer: Shane Chern (University Park) MSC: 11P84 05A17 05A30 PDFBibTeX XMLCite \textit{J. Dousse} and \textit{J. Lovejoy}, Bull. Lond. Math. Soc. 51, No. 2, 193--206 (2019; Zbl 1430.11144) Full Text: DOI arXiv
Kurşungöz, Kağan Andrews-Gordon type series for Capparelli’s and Göllnitz-Gordon identities. (English) Zbl 1414.05042 J. Comb. Theory, Ser. A 165, 117-138 (2019). MSC: 05A19 05A15 05A17 11P84 PDFBibTeX XMLCite \textit{K. Kurşungöz}, J. Comb. Theory, Ser. A 165, 117--138 (2019; Zbl 1414.05042) Full Text: DOI arXiv
Primc, Mirko; Šikić, Tomislav Leading terms of relations for standard modules of the affine Lie algebras \(C_n^{(1)}\). (English) Zbl 1462.17028 Ramanujan J. 48, No. 3, 509-543 (2019). Reviewer: Stefano Capparelli (Roma) MSC: 17B67 17B69 05A19 11P84 PDFBibTeX XMLCite \textit{M. Primc} and \textit{T. Šikić}, Ramanujan J. 48, No. 3, 509--543 (2019; Zbl 1462.17028) Full Text: DOI arXiv
Berkovich, Alexander; Uncu, Ali Kemal Polynomial identities implying Capparelli’s partition theorems. (English) Zbl 1418.05016 J. Number Theory 201, 77-107 (2019). Reviewer: Margherita Maria Ferrari (Tampa) MSC: 05A17 05A15 05A19 11B37 11P83 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{A. K. Uncu}, J. Number Theory 201, 77--107 (2019; Zbl 1418.05016) Full Text: DOI arXiv
Kanade, Shashank; Russell, Matthew C. Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type. (English) Zbl 1409.05018 Electron. J. Comb. 26, No. 1, Research Paper P1.6, 33 p. (2019). MSC: 05A15 05A17 11P84 17B69 PDFBibTeX XMLCite \textit{S. Kanade} and \textit{M. C. Russell}, Electron. J. Comb. 26, No. 1, Research Paper P1.6, 33 p. (2019; Zbl 1409.05018) Full Text: arXiv Link
Fu, Shishuo; Zeng, Jiang A unifying combinatorial approach to refined little Göllnitz and Capparelli’s companion identities. (English) Zbl 1436.11123 Adv. Appl. Math. 98, 127-154 (2018). MSC: 11P81 11P84 05A17 PDFBibTeX XMLCite \textit{S. Fu} and \textit{J. Zeng}, Adv. Appl. Math. 98, 127--154 (2018; Zbl 1436.11123) Full Text: DOI arXiv
Dousse, Jehanne; Lovejoy, Jeremy On a Rogers-Ramanujan type identity from crystal base theory. (English) Zbl 1375.05018 Proc. Am. Math. Soc. 146, No. 1, 55-67 (2018). MSC: 05A17 11P81 11P84 PDFBibTeX XMLCite \textit{J. Dousse} and \textit{J. Lovejoy}, Proc. Am. Math. Soc. 146, No. 1, 55--67 (2018; Zbl 1375.05018) Full Text: DOI arXiv
Cao, Zhu; Chen, Shi-Chao On generalized Schur’s partitions. (English) Zbl 1369.05016 Int. J. Number Theory 13, No. 6, 1381-1391 (2017). Reviewer: Stephan Wagner (Stellenbosch) MSC: 05A17 11P82 11P83 11F37 PDFBibTeX XMLCite \textit{Z. Cao} and \textit{S.-C. Chen}, Int. J. Number Theory 13, No. 6, 1381--1391 (2017; Zbl 1369.05016) Full Text: DOI
Berkovich, Alexander; Uncu, Ali Kemal A new companion to Capparelli’s identities. (English) Zbl 1322.05016 Adv. Appl. Math. 71, 125-137 (2015). MSC: 05A17 05A19 05A20 11B34 11B37 11P83 11P81 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{A. K. Uncu}, Adv. Appl. Math. 71, 125--137 (2015; Zbl 1322.05016) Full Text: DOI arXiv
Bringmann, Kathrin; Mahlburg, Karl False theta functions and companions to Capparelli’s identities. (English) Zbl 1311.05016 Adv. Math. 278, 121-136 (2015). MSC: 05A17 11P84 17B10 PDFBibTeX XMLCite \textit{K. Bringmann} and \textit{K. Mahlburg}, Adv. Math. 278, 121--136 (2015; Zbl 1311.05016) Full Text: DOI arXiv
Dousse, Jehanne A combinatorial proof and refinement of a partition identity of Siladić. (English) Zbl 1284.05334 Eur. J. Comb. 39, 223-232 (2014). MSC: 05E15 05A19 17B67 PDFBibTeX XMLCite \textit{J. Dousse}, Eur. J. Comb. 39, 223--232 (2014; Zbl 1284.05334) Full Text: DOI arXiv
Sills, Andrew V. Rademacher-type formulas for restricted partition and overpartition functions. (English) Zbl 1211.11112 Ramanujan J. 23, No. 1-3, 253-264 (2010). Reviewer: Marvin I. Knopp (Philadelphia) MSC: 11P82 11P84 05A19 PDFBibTeX XMLCite \textit{A. V. Sills}, Ramanujan J. 23, No. 1--3, 253--264 (2010; Zbl 1211.11112) Full Text: DOI
McLaughlin, James; Sills, Andrew V. Ramanujan-Slater type identities related to the moduli 18 and 24. (English) Zbl 1155.05006 J. Math. Anal. Appl. 344, No. 2, 765-777 (2008). Reviewer: Stefano Capparelli (Roma) MSC: 11P84 05A19 33D15 17B67 PDFBibTeX XMLCite \textit{J. McLaughlin} and \textit{A. V. Sills}, J. Math. Anal. Appl. 344, No. 2, 765--777 (2008; Zbl 1155.05006) Full Text: DOI arXiv
Corteel, Sylvie; Lovejoy, Jeremy An iterative-bijective approach to generalizations of Schur’s theorem. (English) Zbl 1139.11043 Eur. J. Comb. 27, No. 4, 496-512 (2006). Reviewer: Tom M. Apostol (Pasadena) MSC: 11P81 05A17 PDFBibTeX XMLCite \textit{S. Corteel} and \textit{J. Lovejoy}, Eur. J. Comb. 27, No. 4, 496--512 (2006; Zbl 1139.11043) Full Text: DOI arXiv
Sills, Andrew V. On series expansions of Capparelli’s infinite product. (English) Zbl 1160.11355 Adv. Appl. Math. 33, No. 2, 397-408 (2004). MSC: 11P81 05A17 05A19 11B65 PDFBibTeX XMLCite \textit{A. V. Sills}, Adv. Appl. Math. 33, No. 2, 397--408 (2004; Zbl 1160.11355) Full Text: DOI arXiv
Berkovich, A.; McCoy, B. M. Generalizations of the Andrews-Bressoud identities for the \(N = 1\) superconformal model \(SM(2, 4\nu )\). (English) Zbl 1185.81112 Math. Comput. Modelling 26, No. 8-10, 37-49 (1997). MSC: 81T40 11P82 11B65 PDFBibTeX XMLCite \textit{A. Berkovich} and \textit{B. M. McCoy}, Math. Comput. Modelling 26, No. 8--10, 37--49 (1997; Zbl 1185.81112) Full Text: DOI arXiv
Capparelli, Stefano A construction of the level 3 modules for the affine Lie algebra \(A_ 2^{(2)}\) and a new combinatorial identity of the Rogers-Ramanujan type. (English) Zbl 0862.17017 Trans. Am. Math. Soc. 348, No. 2, 481-501 (1996). Reviewer: M.Primc (Zagreb) MSC: 17B67 05A19 PDFBibTeX XMLCite \textit{S. Capparelli}, Trans. Am. Math. Soc. 348, No. 2, 481--501 (1996; Zbl 0862.17017) Full Text: DOI
Tamba, Manvendra; Xie, Chuanfu Level three standard modules \(A^{(2)}_ 2\) and combinatorial identities. (English) Zbl 0854.17029 J. Pure Appl. Algebra 105, No. 1, 53-92 (1995). Reviewer: Stefano Capparelli (Roma) MSC: 17B67 05A19 PDFBibTeX XMLCite \textit{M. Tamba} and \textit{C. Xie}, J. Pure Appl. Algebra 105, No. 1, 53--92 (1995; Zbl 0854.17029) Full Text: DOI
Andrews, George E. The death of proof? Semi-rigorous mathematics? You’ve got to be kidding! (English) Zbl 1019.00501 Math. Intell. 16, No. 4, 16-18 (1994). MSC: 00A30 PDFBibTeX XMLCite \textit{G. E. Andrews}, Math. Intell. 16, No. 4, 16--18 (1994; Zbl 1019.00501) Full Text: DOI