Finite Difference Calculus for Alternating Permutations

TL;DR

This paper reinterprets a finite difference system within the context of alternating permutations, enabling joint analysis of tangent and secant trees and introducing a new permutation statistic for generating polynomials.

Contribution

It introduces a novel application of finite difference calculus to alternating permutations and defines a new statistic for generating polynomial calculations.

Findings

Unified approach to tangent and secant trees

New statistic for permutation analysis

Explicit generating polynomial formulas

Abstract

The finite difference equation system introduced by Christiane Poupard in the study of tangent trees is reinterpreted in the alternating permutation environment. It makes it possible to make a joint study of both tangent and secant trees and calculate the generating polynomial for alternating permutations by a new statistic, referred to as being the greater neighbor of the maximum.