Séminaire lotharingien de combinatoire, Tome 65 (2011-2012)
Citer cet article
Philippe Biane; Luigi Cantini; Andrea Sportiello. Doubly-Refined Enumeration of Alternating Sign Matrices and Determinants of 2-Staircase Schur Functions. Séminaire lotharingien de combinatoire, Tome 65 (2011-2012). http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a5/
@article{SLC_2011-2012_65_a5,
author = {Philippe Biane and Luigi Cantini and Andrea Sportiello},
title = {Doubly-Refined {Enumeration} of {Alternating} {Sign} {Matrices} and {Determinants} of {2-Staircase} {Schur} {Functions}},
journal = {S\'eminaire lotharingien de combinatoire},
year = {2011-2012},
volume = {65},
url = {http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a5/}
}
TY - JOUR
AU - Philippe Biane
AU - Luigi Cantini
AU - Andrea Sportiello
TI - Doubly-Refined Enumeration of Alternating Sign Matrices and Determinants of 2-Staircase Schur Functions
JO - Séminaire lotharingien de combinatoire
PY - 2011-2012
VL - 65
UR - http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a5/
ID - SLC_2011-2012_65_a5
ER -
%0 Journal Article
%A Philippe Biane
%A Luigi Cantini
%A Andrea Sportiello
%T Doubly-Refined Enumeration of Alternating Sign Matrices and Determinants of 2-Staircase Schur Functions
%J Séminaire lotharingien de combinatoire
%D 2011-2012
%V 65
%U http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a5/
%F SLC_2011-2012_65_a5
We prove a determinantal identity concerning Schur functions for 2-staircase diagrams \lambda=(ln+l',ln,l(n-1)+l',l(n-1),...,l+l',l,l',0). When l=1 and l'=0 these functions are related to the partition function of the 6-vertex model at the combinatorial point and hence to enumerations of Alternating Sign Matrices. A consequence of our result is an identity concerning the doubly-refined numbers of Alternating Sign Matrices.
