Double deficiencies of Dyck paths via the Billey-Jockusch-Stanley bijection

2017/08/16 by Martin Rubey, Christian Stump, Rubey, Martin +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1708.05092

arxiv created 2017/08/16 · openalex publication_date 2017/08/16 · arxiv updated 2017/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a recent conjecture by René Marczinzik involving certain statistics on Dyck paths that originate in the representation theory of Nakayama algebras of a linearly oriented quiver. We do so by analysing the effect of the Billey-Jockusch-Stanley bijection between Dyck paths and 321-avoiding permutations on these statistics, which was suggested by the result of a query issued to the online database FindStat.

Cited by

• A survey on Auslander-Gorenstein algebras

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