Bessel polynomials, double factorials and context-free grammars
The purpose of this paper is to show that Bessel polynomials, double factorials and Catalan triangle can be generated by using context-free grammars.
math.CO↗
arXiv subjects
Shi-Mei Ma
Publications and source records attributed to Shi-Mei Ma.
Some combinatorial sequences associated with context-free grammars
The purpose of this paper is to show that some combinatorial sequences, such as second-order Eulerian numbers and Eulerian numbers of type $B$, can be generated by context-free grammars.
math.CO↗
Polynomials with only real zeros and the Eulerian polynomials of type D
A remarkable identity involving the Eulerian polynomials of type D was obtained by Stembridge (Adv. Math. 106 (1994), p. 280, Lemma 9.1). In this paper we explore an equivalent form of this identity. We prove Brenti's real-rootedness conjecture for the Eulerian polynomials of type $D$.
math.CO↗
A family of two-variable derivative polynomials for tangent and secant
In this paper we introduce a family of two-variable derivative polynomials for tangent and secant. We study the generating functions for the coefficients of this family of polynomials. In particular, we establish a connection between these generating functions and Eulerian polynomials.
math.CO↗
Derivative polynomials and permutations by numbers of interior peaks and left peaks
Derivative polynomials in two variables are defined by repeated differentiation of the tangent and secant functions. We establish the connections between the coefficients of these derivative polynomials and the numbers of interior and left peaks over the symmetric group. Properties of the generating functions for the numbers of interior and left peaks over the symmetric group, including recurrence relations, generating functions and real-rootedness, are studied.
math.CO↗
An explicit formula for the number of permutations with a given number of alternating runs
Let $R(n,k)$ denote the number of permutations of ${1,2,...,n}$ with $k$ alternating runs. In this note we present an explicit formula for the numbers $R(n,k)$.
math.CO↗