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pro vyhledávání: '"A. Bressoud"'
We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we give an explicit weight- and length-preserving bijection between sets
Externí odkaz:
http://arxiv.org/abs/2403.05414
Akademický článek
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In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ for $j=0$ or $1$. In this paper, we introduce a new partition function $\overline{B}_0$ which can be viewed as an overpartition analogue of the partition function $B_0$. An overpartitio
Externí odkaz:
http://arxiv.org/abs/2312.00466
Autor:
Agarwal, Archit1 (AUTHOR) phd2001241002@iiti.ac.in, Bhoria, Subhash Chand2 (AUTHOR), Eyyunni, Pramod1 (AUTHOR), Maji, Bibekananda1 (AUTHOR)
Publikováno v:
Annals of Combinatorics. Jun2024, Vol. 28 Issue 2, p555-574. 20p.
We present what we call a "motivated proof" of the Bressoud-G\"ollnitz-Gordon partition identities. Similar "motivated proofs" have been given by Andrews and Baxter for the Rogers-Ramanujan identities and by Lepowsky and Zhu for Gordon's identities.
Externí odkaz:
http://arxiv.org/abs/2311.01992
Autor:
Russell, Matthew C.
We find bivariate generating functions for the $k=1$ cases of recently conjectured colored partition identities of Capparelli, Meurman, A. Primc, and M. Primc that are slight variants of the generating functions for the sum sides of the Andrews-Gordo
Externí odkaz:
http://arxiv.org/abs/2306.16251
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity
Externí odkaz:
http://arxiv.org/abs/2210.03457
Publikováno v:
Taiwanese Journal of Mathematics, 2017 Dec 01. 21(6), 1233-1263.
Externí odkaz:
https://www.jstor.org/stable/90016075
Autor:
Wieczorek, Maggie
The Andrews-Bressoud identities are one of many families of $q$-series identities relating an infinite sum to an infinite product. While the original motivation for studying these series relates to partitions, they can also be viewed in relation to i
Externí odkaz:
http://arxiv.org/abs/2002.07846
Autor:
Zhou, Yue
In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem or the $q$-Dyson constant term identity. This conjecture was proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. In
Externí odkaz:
http://arxiv.org/abs/2009.05365