Geodesic
Decorated Dyck Paths and the Delta Conjecture
Séminaire lotharingien de combinatoire, 80B (2018)

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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). 

@article{SLC_2018_80B_a33,
     author = {Michele D'Adderio and Anna Vanden Wyngaerd},
     title = {Decorated {Dyck} {Paths} and the {Delta} {Conjecture}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a33/}
}
TY  - JOUR
AU  - Michele D'Adderio
AU  - Anna Vanden Wyngaerd
TI  - Decorated Dyck Paths and the Delta Conjecture
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a33/
ID  - SLC_2018_80B_a33
ER  - 
%0 Journal Article
%A Michele D'Adderio
%A Anna Vanden Wyngaerd
%T Decorated Dyck Paths and the Delta Conjecture
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a33/
%F SLC_2018_80B_a33
Michele D'Adderio; Anna Vanden Wyngaerd. Decorated Dyck Paths and the Delta Conjecture. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a33/