Geodesic
Doubly-Refined Enumeration of Alternating Sign Matrices and Determinants of 2-Staircase Schur Functions
Séminaire lotharingien de combinatoire, Tome 65 (2011-2012)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@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},
     publisher = {mathdoc},
     volume = {65},
     year = {2011-2012},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a5/
%F SLC_2011-2012_65_a5
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/