9 citations · 49 across the 59 of their papers we have counts for
59 papers · 1 filter
Binomial expansions of Jacobi-Stirling numbers and real-rootedness of Jacobi-Stirling descent polynomials
Shi-Mei Ma, Ming-Xin Wang
In this paper, we first expand fixed diagonals of the Jacobi-Stirling numbers in a binomial basis. For the second kind, the expansion coefficients are polynomials in with non…
Eulerian insertion operators and an Eulerian form of the Pieri rule
Shi-Mei Ma
We study the operators obtained by inserting copies of a new largest letter into multiset permutations. Let denote the operator which inserts copies of a new largest lett…
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…
The half interlacing property among the types A, B and D Eulerian polynomials
Shi-Mei Ma
A famous result in the theory of combinatorial polynomials is the real-rootedness of the type Eulerian polynomial , which was originally conjectured by Brenti in 1994.…
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…
A symmetric decomposition of the Boros-Moll polynomials
Guo-Niu Han, Shi-Mei Ma, Yeong-Nan Yeh
In their study of a quartic integral, Boros and Moll introduced a special case of Jacobi polynomials, which are now known as the Boros-Moll polynomials. In this paper, we study a s…
Commuting Eulerian operators
Shi-Mei Ma, Hao Qi, Jean Yeh +1
Motivated by the work of Visontai and Dey-Sivasubramanian on the gamma-positivity of some polynomials, we find the commutative property of a pair of Eulerian operators. As an appli…
Stirling permutation codes
Shi-Mei Ma, Hao Qi, Jean Yeh +1
The development of the theories of the second-order Eulerian polynomials began with the works of Buckholtz and Carlitz in their studies of an asymptotic expansion. Gessel-Stanley i…
Recurrences for the derivative polynomials for tangent and secant
Guo-Niu Han, Shi-Mei Ma
In this paper, we choose the derivative polynomials for tangent and secant as basis sets of polynomial space. From this viewpoint, we first give an expansion of the derivative poly…
Alternating runs of permutations and the central factorial numbers
Qi Fang, Ya-Nan Feng, Shi-Mei Ma
Let R(n,k) be the number of permutations of with k alternating runs. In this paper, we establish the relationships between R(n,k) and the central factorial numbe…
Positivity of Narayana polynomials and Eulerian polynomials
Shi-Mei Ma, Hao Qi, Jean Yeh +1
Gamma-positivity appears frequently in finite geometries, combinatorics and number theory. Motivated by the recent work of Sagan and Tirrell (Adv. Math., 374 (2020), 107387), we st…
Eulerian polynomials, Stirling permutations and increasing trees
Shi-Mei Ma, Jun Ma, Jean Yeh +1
We study two generalizations of the gamma-expansion of Eulerian polynomials from the viewpoint of the decompositions of statistics. We first present an expansion formula of the tri…
Excedance-type polynomials and gamma-positivity
Shi-Mei Ma, Jun Ma, Jean Yeh +1
The object of this paper is to give a systematic treatment of excedance-type polynomials. We first give a sufficient condition for a sequence of polynomials to have alternatingly i…
Alternating Eulerian polynomials and left peak polynomials
Shi-Mei Ma, Qi Fang, Toufik Mansour +1
In this paper we present grammatical interpretations of the alternating Eulerian polynomials of types A and B. As applications, we derive several properties of the type B alternati…
Positivity and divisibility of alternating descent polynomials
Zhicong Lin, Shi-Mei Ma, David G. L. Wang +1
The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations…
Eulerian pairs and Eulerian recurrence systems
Shi-Mei Ma, Jun Ma, Jean Yeh +1
In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of seve…