Covering relations of k-Grassmannian permutations of type B

TL;DR

This paper characterizes the covering relations in the Bruhat order of type B maximal parabolic quotients using combinatorial methods based on signed permutations, providing a detailed classification and answering a previously open question.

Contribution

It offers a combinatorial classification of covering relations in the Bruhat order for type B Grassmannian permutations, addressing an open problem in the field.

Findings

Four types of covering relation pairs identified

Provides a combinatorial model for type B maximal parabolic quotients

Answers a question by Ikeda and Matsumura

Abstract

The main result of this work is the characterization of the covering relations of the Bruhat order of the maximal parabolic quotients of type B. Our approach is mainly combinatorial and is based in the pattern of the corresponding permutations also called signed $k$-Grassmannians permutations. We obtain that a covering relation can be classified in four different pairs of permutations. This answers a question raised by Ikeda and Matsumura providing a nice combinatorial model for maximal parabolic quotients of type B.