An explicit derivation of the Mobius function for Bruhat order

TL;DR

This paper provides an explicit, nonrecursive method to derive the Mobius function for intervals in the Bruhat order of Coxeter groups, offering a new perspective on a classical combinatorial result.

Contribution

It introduces a complete matching for the Hasse diagram of Bruhat order intervals, enabling a novel derivation of the Mobius function that is explicit and nonrecursive.

Findings

Provides a new explicit derivation of the Mobius function

Offers a complete matching for the Hasse diagram of Bruhat order

Recovers classical results by Verma

Abstract

We give an explicit nonrecursive complete matching for the Hasse diagram of the strong Bruhat order of any interval in any Coxeter group. This yields a new derivation of the Mobius function, recovering a classical result due to Verma.