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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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