Geodesic
Combinatorial Bases of Polynomials
Séminaire lotharingien de combinatoire, 80B (2018)

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We establish a poset structure on combinatorial bases of polynomials, defined by positive expansions. These bases include the well-studied Schubert polynomials, Demazure characters and Demazure atoms, as well as the recently-introduced slide and quasi-key bases. The product of a Schur polynomial and an element of a basis in the poset expands positively in that basis; in particular we give the first Littlewood-Richardson rule for the product of a Schur polynomial and a quasi-key polynomial, extending the rule of Haglund, Luoto, Mason and van Willigenburg for quasi-Schur polynomials. We also establish a bijection connecting the combinatorial models of semi-skyline fillings and quasi-key tableaux for these polynomials. 

@article{SLC_2018_80B_a52,
     author = {Dominic Searles},
     title = {Combinatorial {Bases} of {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a52/}
}
TY  - JOUR
AU  - Dominic Searles
TI  - Combinatorial Bases of Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a52/
ID  - SLC_2018_80B_a52
ER  - 
%0 Journal Article
%A Dominic Searles
%T Combinatorial Bases of Polynomials
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a52/
%F SLC_2018_80B_a52
Dominic Searles. Combinatorial Bases of Polynomials. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a52/