Descent polynomials for k bubble-sortable permutations of type B

TL;DR

This paper introduces a type B analog of bubble sort and maximum drop statistic, providing enumeration formulas for signed permutations with constraints, and reveals a connection to 2-colored juggling sequences.

Contribution

It defines a new type B bubble sort and maximum drop statistic, and derives enumeration formulas for related signed permutations, linking combinatorics and juggling sequences.

Findings

Explicit enumeration formulas for signed permutations with bounded descents and drop.

Recursive and generating function formulas for these permutations.

Connection established between signed permutations and 2-colored juggling sequences.

Abstract

Motivated by the work of Chung, Claesson, Dukes, and Graham, we define a natural type B analog of the classic bubble sort, and use it to define a type B analog of the maximum drop statistic. We enumerate (by explicit, recursive, and generating function formulas) signed permutations with r type B descents and type B maximum drop at most k. We also find a connection between these signed permutations and certain 2-colored juggling sequences.