Journal of Integer Sequences, Vol. 20 (2017), Article 17.9.6

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

Christian Stump
Institut für Mathematik
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin


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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