Geodesic
Delta Operators at q=1 and Polyominoes
Séminaire lotharingien de combinatoire, 80B (2018)

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For a symmetric function G, the Delta operator ΔG is defined via its action on modified Macdonald polynomials by setting ΔGH~μ = G[Bμ], where Bμ is a polynomial in q and t. Previous work by Haglund, Remmel, Wilson conjectures a combinatorial interpretation for Δeken, generalizing the Shuffle Theorem. Here, we prove combinatorial interpretations for Δmλen|q=1 and Δsλen|q=1, expressing each as weighted sum over (parallelogram) polyominoes in a rectangle, and provide an explicit combinatorial interpretation for their elementary and Schur function expansions. 

@article{SLC_2018_80B_a76,
     author = {Angela Hicks and Marino Romero},
     title = {Delta {Operators} at q=1 and {Polyominoes}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a76/}
}
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AU  - Angela Hicks
AU  - Marino Romero
TI  - Delta Operators at q=1 and Polyominoes
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a76/
ID  - SLC_2018_80B_a76
ER  - 
%0 Journal Article
%A Angela Hicks
%A Marino Romero
%T Delta Operators at q=1 and Polyominoes
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a76/
%F SLC_2018_80B_a76
Angela Hicks; Marino Romero. Delta Operators at q=1 and Polyominoes. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a76/