10 papers
A general method of deducing the determinantal expressions for polynomial and its derivative
Hongyi Lou, Shi-Mei Ma, Xinzhe Song +2
In this paper, we present a general method of deducing the determinantal expressions for a polynomial and its derivative. As illustrations, we provide three determinantal expressio…
Eulerian-type polynomials over matchings and matching permutations
Shi-Mei Ma, Sergey Kitaev, Jean Yeh +1
Claesson and Linusson [Proc. Am. Math. Soc., 139 (2011), 435-449] observed that there are n! matchings on [2n] with no left-nestings. Inspired by this result, this paper is devoted…
Symmetric decompositions and Euler-Stirling statistics on Stirling permutations
Shi-Mei Ma, Jianfeng Wang, Guiying Yan +2
The Stirling permutations introduced by Gessel-Stanley have recently received considerable attention. Motivated by Ji's work on -Eulerian polynomials (Sci China Math., 2025)…
Eulerian-type polynomials over Stirling permutations and box sorting algorithm
Shi-Mei Ma, Jun-Ying Liu, Jean Yeh +1
It is well known that ascents, descents and plateaux are equidistributed over the set of classical Stirling permutations. Their common enumerative polynomials are the second-order…
Determinantal representations of alternating run polynomials
Shi-Mei Ma, Hong Bian, Jun-Ying Liu +2
Based on a determinantal formula for the higher derivative of a quotient of two functions, we first present the determinantal expressions of Eulerian polynomials and Andre polynomi…
A curious symmetric decomposition of the (des, exc)-Eulerian polynomials
Shi-Mei Ma, Toufik Mansour, Yeong-Nan Yeh
One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the wo…
Stirling permutation codes. II
Shi-Mei Ma, Hao Qi, Jean Yeh +1
In the context of Stirling polynomials, Gessel and Stanley introduced the definition of Stirling permutation, which has attracted extensive attention over the past decades. Recentl…
Normal ordered grammars
Shi-Mei Ma, Toufik Mansour, Jean Yeh +1
We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered gram…
On the joint distributions of succession and Eulerian statistics
Shi-Mei Ma, Hao Qi, Jean Yeh +1
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of desc…
Differential operators, grammars and Young tableaux
Shi-Mei Ma, Jean Yeh, Yeong-Nan Yeh
In algebraic combinatorics and formal calculation, context-free grammar is defined by a formal derivative based on a set of substitution rules. In this paper, we investigate this i…