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Involutions under Bruhat order and labeled Motzkin Paths
- Publication Year :
- 2021
-
Abstract
- In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a recently introduced interpretation of this rank generating function in terms of visible inversions. By restricting our identity to fixed-point-free (FPF) involutions, we recover an identity due to Louis Billera, Lionel Levine and Karola M\'esz\'aros with a previous bijective proof by Matthew Watson. Our work sheds new light on the Ethiopian dinner game.<br />Comment: 7 pages
- Subjects :
- Mathematics - Combinatorics
05A19
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2106.06021
- Document Type :
- Working Paper