Andre Permutation Calculus; a Twin Seidel Matrix Sequence

TL;DR

This paper introduces a matrix-analog refinement of tangent and secant numbers based on Entringer numbers within André permutations, providing new generating functions for related statistics.

Contribution

It constructs a novel matrix-analog refinement of tangent and secant numbers and derives closed-form exponential generating functions for Entringerian statistics.

Findings

Matrix-analog refinement of tangent and secant numbers

Closed expressions for three-variate exponential generating functions

Enhanced understanding of Entringer numbers in André permutations

Abstract

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 three-variate exponential generating functions for pairs of so-called Entringerian statistics are derived.