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pro vyhledávání: '"Zhong, Michael X. X."'
In this note, we apply the power-partible reduction to show the following arithmetic properties of large Schr\"oder polynomials $S_n(z)$ and little Schr\"oder polynomials $s_n(z)$: for any odd prime $p$, nonnegative integer $r\in\mathbb{N}$, $\vareps
Externí odkaz:
http://arxiv.org/abs/2310.06314
Autor:
Wang, Rong-Hua, Zhong, Michael X. X.
In this paper, we introduce the power-partible reduction for holonomic (or, P-recursive) sequences and apply it to obtain a series of congruences for Ap\'ery numbers $A_k$. In particular, we prove that, for any $r\in\mathbb{N}$, there exists an integ
Externí odkaz:
http://arxiv.org/abs/2301.01985
Autor:
Wang, Rong-Hua, Zhong, Michael X. X.
Polynomial reduction, designed first for hypergeometric terms, can be used to automatically prove and generate new hypergeometric identities from old ones. In this paper, we extend the reduction method to holonomic sequences. As applications, we desc
Externí odkaz:
http://arxiv.org/abs/2205.11129
Autor:
Wang, Rong-Hua, Zhong, Michael X. X.
In this paper, we present a $q$-analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the $q$-Gosper representation, we describe the structure of rational functions that are summable when multiplied with
Externí odkaz:
http://arxiv.org/abs/2203.16047
Autor:
Wang, Rong-Hua, Zhong, Michael X. X.
During the study of dual sequences, Sun introduced the polynomials \[ D_n(x,y)=\sum_{k=0}^{n}{n\choose k}{x\choose k}y^k\text{ and } S_n(x,y)=\sum_{k=0}^{n}\binom{n}{k}\binom{x}{k}\binom{-1-x}{k} y^k. \] Many related congruences have been established
Externí odkaz:
http://arxiv.org/abs/2010.04439
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Using equivariant cohomology theory, Naruse obtained a hook length formula for the number of standard Young tableaux of skew shape $\lambda/\mu$. Morales, Pak and Panova found two $q$-analogues of Naruse's formula respectively by counting semistandar
Externí odkaz:
http://arxiv.org/abs/1711.03048
Anderson established a connection between core partitions and order ideals of certain posets by mapping a partition to its $\beta$-set. In this paper, we give a characterization of the poset $P_{(s,s+1,s+2)}$ whose order ideals correspond to $(s,s+1,
Externí odkaz:
http://arxiv.org/abs/1406.2583
Let $S_n$ denote the symmetric group on $\{1,2,\ldots,n\}$. For two permutations $u, v\in S_n$ such that $u\leq v$ in the Bruhat order, let $R_{u,v}(q)$ and $\R_{u,v}(q)$ denote the Kazhdan-Lusztig $R$-polynomial and $\R$-polynomial, respectively. Le
Externí odkaz:
http://arxiv.org/abs/1312.2170
Publikováno v:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM; Oct2024, Vol. 118 Issue 4, p1-10, 10p