Séminaire lotharingien de combinatoire, 54A (2005-2007)
Citer cet article
Cristina M. Ballantine; Rosa C. Orellana. A Combinatorial Interpretation for the Coefficients in the Kronecker Product s(n-p,p)*s\lambda. Séminaire lotharingien de combinatoire, 54A (2005-2007). http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a5/
@article{SLC_2005-2007_54A_a5,
author = {Cristina M. Ballantine and Rosa C. Orellana},
title = {A {Combinatorial} {Interpretation} for the {Coefficients} in the {Kronecker} {Product} s(n-p,p)*s\lambda},
journal = {S\'eminaire lotharingien de combinatoire},
year = {2005-2007},
volume = {54A},
url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a5/}
}
TY - JOUR
AU - Cristina M. Ballantine
AU - Rosa C. Orellana
TI - A Combinatorial Interpretation for the Coefficients in the Kronecker Product s(n-p,p)*s\lambda
JO - Séminaire lotharingien de combinatoire
PY - 2005-2007
VL - 54A
UR - http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a5/
ID - SLC_2005-2007_54A_a5
ER -
%0 Journal Article
%A Cristina M. Ballantine
%A Rosa C. Orellana
%T A Combinatorial Interpretation for the Coefficients in the Kronecker Product s(n-p,p)*s\lambda
%J Séminaire lotharingien de combinatoire
%D 2005-2007
%V 54A
%U http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a5/
%F SLC_2005-2007_54A_a5
In this paper we give a combinatorial interpretation for the coefficient of s\nu in the Kronecker product s(n-p,p)*s\lambda, where \lambda=(\lambda1, ..., \lambdal(\lambda)) is a partition of n, if l(\lambda)>=2p-1 or \lambda1>=2p-1; that is, if \lambda is not a partition inside the 2(p-1) x 2(p-1) square. For \lambda inside the square our combinatorial interpretation provides an upper bound for the coefficients. In general, we are able to combinatorially compute these coefficients for all \lambda when n>(2p-2)2. We use this combinatorial interpretation to give characterizations for multiplicity free Kronecker products. We have also obtained some formulas for special cases.
Corrigendum
On page 25, line -6, in Corollary 4.13, $ \displaystyle m_4=\min\left\{ s,p-s, \left\lfloor\frac{p+s-t}{2}\right\rfloor\right\}$ should be replaced by $ \displaystyle m_4=\min\left\{ s,p-s-1, \left\lfloor\frac{p+s-t}{2}\right\rfloor\right\}$.
