相关论文: Parity-Alternate Permutations and Signed Eulerian …

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

We study generating functions for the number of even (odd) permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function…

The powers of matrices with Stirling number-coefficients are investigated. It is revealed that the elements of these matrices have a number of properties of the ordinary Stirling numbers. Moreover, "higher order" Bell, Fubini and Eulerian…

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…

In this paper we investigate some new problems in additive combinatorics. Our problems mainly involve permutations (or circular permutations) $n$ distinct numbers (or elements of an additive abelian group) $a_1,\ldots,a_n$ with adjacent…

Many important statistics of signed permutations are realized in the corresponding permutation tableaux or bare tableaux of type $B$: Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation…

We define the $m$th-order Eulerian numbers with a combinatorial interpretation. The recurrence relation of the $m$th-order Eulerian numbers, the row generating function and the row sums of the $m$th-order Eulerian triangle are presented. We…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

In an award-winning expository article, V. Pozdnyakov and J.M. Steele gave a beautiful demonstration of the ramifications of a basic bijection for permutations. The aim of this note is to connect this correspondence to a seemingly unrelated…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

This paper is concerned with multivariate refinements of the gamma-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and…

We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.

One of the interesting features about field theories in odd dimensions is the induction of parity violating terms and well-defined {\em finite} topological actions via quantum loops if a fermion mass term is originally present and…

Noticing that some recent variations of descent polynomials are special cases of Carlitz and Scoville's four-variable polynomials, which enumerate permutations by the parity of descent and ascent positions, we prove a $q$-analogue of…

In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…

We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Straub's analog of Euler's Odd-Distinct partition theorem. We…

This paper is continuation of the systematic study of distribution of quadrant marked mesh patterns. We study quadrant marked mesh patterns on up-down and down-up permutations, also known as alternating and reverse alternating permutations,…

We prove that an odd number is an Euler pseudoprime for exactly one half of the admissible bases if and only if it is a special Carmichael number.

Entringer numbers occur in the Andr\'e permutation combinatorial set-up under several forms. This leads to the construction of a matrix-analog refinement of the tangent (resp. secant) numbers. Furthermore, closed expressions for the…

An odd prime labeling is a variation of a prime labeling in which the vertices of a graph of order~$n$ are labeled with the distinct odd integers $1$ to $2n-1$ so that the labels of adjacent vertices are relatively prime. This paper…