Expected Value of Statistics on Type-B Permutation Tableaux

TL;DR

This paper calculates the expected values of various statistics on Type-B permutation tableaux, linking combinatorial properties with the PASEP model, and extending previous work on permutation tableaux.

Contribution

It introduces new expected value computations for statistics on Type-B permutation tableaux, connecting combinatorics with stochastic processes.

Findings

Expected number of rows and unrestricted rows computed

Expected number of diagonal ones determined

Expected adjacent south and west steps calculated

Abstract

Type-B permutation tableaux are combinatorial objects introduced by Lam and Williams that have an interesting connection with the partially asymmetric simple exclusion process (PASEP). In this paper, we compute the expected value of several statistics on these tableaux. Some of these computations are motivated by a similar paper on permutation tableaux. Others are motivated by the PASEP. In particular, we compute the expected number of rows, unrestricted rows, diagonal ones, adjacent south steps, and adjacent west steps.