Double Deficiencies of Dyck Paths via the Billey-Jockusch-Stanley Bijection
Martin Rubey
Fakultät für Mathematik und Geoinformation
Technische Universität Wien
Wiedner Hauptstr. 8-10
1040 Wien
Austria
Christian Stump
Institut für Mathematik
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin
Germany
Abstract:
We prove a recent conjecture by 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 analyzing 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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(Concerned with sequences
A001006
A005043.)
Received August 17 2017; revised versions received October 19 2017;
October 22 2017.
Published in Journal of Integer Sequences, October 27 2017.
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