Séminaire Lotharingien de Combinatoire, 80B.34 (2018), 12 pp.
Michele D'Adderio and Anna Vanden Wyngaerd
Decorated Dyck Paths and the Delta Conjecture
Abstract.
We discuss the combinatorics of the decorated Dyck paths appearing in the Delta conjecture framework in (Haglund et al 2015) and (Zabrocki 2016), by introducing two new statistics,
bounce and bounce'. We then provide plethystic formulae for their q,t-enumerators, by proving in this way a decorated version of Haglund's q,t-Schröder theorem, answering a question in (Haglund et al. 2015). In particular we provide both an algebraic and a combinatorial explanation of a symmetry conjecture in (Haglund et al. 2015) and (Zabrocki 2016).
This is an extended abstract of (D'Adderio, Vanden Wyngaerd 2017).
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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