Theta-vexillary signed permutations

TL;DR

This paper characterizes theta-vexillary signed permutations in the hyperoctahedral group, linking their structure to degeneracy loci, Rothe diagram corners, and pattern avoidance, providing multiple perspectives on their properties.

Contribution

It introduces new characterizations of theta-vexillary signed permutations using corners in Rothe diagrams and pattern avoidance, expanding understanding of their combinatorial structure.

Findings

Characterizations via Rothe diagram corners

Pattern avoidance criteria for theta-vexillary permutations

Connections to degeneracy loci in type B and C

Abstract

Theta-vexillary signed permutations are elements in the hyperoctahedral group that index certain classes of degeneracy loci of type B and C. These permutations are described using triples of $s$-tuples of integers subject to specific conditions. The objective of this work is to present different characterizations of theta-vexillary signed permutations, describing them in terms of corners in the Rothe diagram and pattern avoidance.