Double deficiencies of Dyck paths via the Billey-Jockusch-Stanley bijection
Martin Rubey, Christian Stump
TL;DR
This paper proves a conjecture relating to Dyck path statistics derived from representation theory, using the Billey-Jockusch-Stanley bijection to analyze the effect on these statistics.
Contribution
It establishes a proof of a conjecture connecting Dyck path statistics and representation theory through bijection analysis.
Findings
Confirmed the conjecture involving Dyck path statistics
Analyzed the Billey-Jockusch-Stanley bijection's impact on these statistics
Linked combinatorial structures to representation theory insights
Abstract
We prove a recent conjecture by Ren\'e 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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry