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pro vyhledávání: '"He, Thomas Y."'
In this article, we first investigate the partitions whose parts are congruent to $a$ or $b$ modulo $k$ with the aid of separable integer partition classes with modulus $k$ introduced by Andrews. Then, we introduce the $(k,r)$-overpartitions in which
Externí odkaz:
http://arxiv.org/abs/2406.19823
Autor:
Chen, Y. H., He, Thomas Y.
Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(
Externí odkaz:
http://arxiv.org/abs/2405.19918
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
Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer partition classes
Externí odkaz:
http://arxiv.org/abs/2305.13151
Autor:
He, Thomas Y., Zhao, Alice X. H.
The G\"ollnitz-Gordon identities were found by G\"ollnitz and Gordon independently. In 1967, Andrews obtained a combinatorial generalization of the G\"ollnitz-Gordon identities, called the Andrews-G\"ollnitz-Gordon theorem. In 1980, Bressoud extended
Externí odkaz:
http://arxiv.org/abs/2203.03257
Publikováno v:
In European Journal of Combinatorics May 2024 118
Publikováno v:
European Journal of Combinatorics (2024)
The main objective of this paper is to present an answer to Bressoud's conjecture for the case $j=0$, resulting in a complete solution to the conjecture. The case for $j=1$ has been recently resolved by Kim. Using the connection established in our pr
Externí odkaz:
http://arxiv.org/abs/2001.00162
In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ for $j=0$ or $1$, where the function $A_j$ counts the number of partitions with certain congruence conditions and the function $B_j$ counts the number of partitions with certain differe
Externí odkaz:
http://arxiv.org/abs/1910.08224
Publikováno v:
In Advances in Mathematics 6 August 2022 404 Part A
We give an overpartition analogue of Bressoud's combinatorial generalization of the G\"ollnitz-Gordon theorem for even moduli in general case. Let $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain difference
Externí odkaz:
http://arxiv.org/abs/1702.08621