Quadrant marked mesh patterns in alternating permutations II

TL;DR

This paper continues the exploration of quadrant marked mesh patterns, focusing on their distribution in up-down and down-up permutations, expanding the understanding of pattern occurrences in these permutation classes.

Contribution

It extends previous work by analyzing the distribution of quadrant marked mesh patterns specifically in alternating permutations, providing new insights into their combinatorial properties.

Findings

Distribution formulas for quadrant marked mesh patterns in alternating permutations

Characterization of pattern occurrences in up-down and down-up permutations

Extension of previous pattern distribution results

Abstract

This paper is continuation of the systematic study of distribution of quadrant marked mesh patterns initiated in "S. Kitaev and J. Remmel, Quadrant marked mesh patterns, J. Integer Sequences 12, Issue 4 (2012), Article 12.4.7.". We study quadrant marked mesh patterns on up-down and down-up permutations.