Skip to main content
Open Access Publications from the University of California

Combinatorial Theory

Combinatorial Theory banner

Odd diagrams, Bruhat order, and pattern avoidance

Published Web Location Commons 'BY' version 4.0 license

The odd diagram of a permutation is a subset of the classical diagram with additional parity conditions. In this paper, we study classes of permutations with the same odd diagram, which we call odd diagram classes. First, we prove a conjecture relating odd diagram classes and 213- and 312-avoiding permutations. Secondly, we show that each odd diagram class is a Bruhat interval. Instrumental to our proofs is an explicit description of the Bruhat edges that link permutations in a class.

Mathematics Subject Classifications: 05A05, 05A15

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View