Prism permutations in the Bruhat order

TL;DR

This paper introduces prism permutations, a new class of elements in Coxeter groups, and explores their properties, characterizations, and a novel concept called calibration in permutation patterns.

Contribution

It defines prism permutations as a generalization of boolean elements, providing new characterizations and introducing the concept of calibration in permutation patterns.

Findings

Prism permutations are characterized by reduced words and pattern containment.

The notion of calibration is introduced for permutation patterns.

Prism permutations extend the understanding of Coxeter group elements.

Abstract

The boolean elements of a Coxeter group have been characterized and shown to possess many interesting properties and applications. Here we introduce "prism permutations," a generalization of those elements, characterizing the prism permutations equivalently in terms of their reduced words and in terms of pattern containment. As part of this work, we introduce the notion of "calibration" to permutation patterns.