TY - JOUR
T1 - A bijection between dominant Shi regions and core partitions
AU - Fishel, Susanna
AU - Vazirani, Monica
PY - 2010/12
Y1 - 2010/12
N2 - It is well-known that Catalan numbers Cn=1n+1(2nn) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n+1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi arrangement and partitions which are both n-cores as well as (mn+1)-cores. The bijection is natural in the sense that it commutes with the action of the affine symmetric group.
AB - It is well-known that Catalan numbers Cn=1n+1(2nn) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n+1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi arrangement and partitions which are both n-cores as well as (mn+1)-cores. The bijection is natural in the sense that it commutes with the action of the affine symmetric group.
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U2 - 10.1016/j.ejc.2010.05.014
DO - 10.1016/j.ejc.2010.05.014
M3 - Article
AN - SCOPUS:77956182400
SN - 0195-6698
VL - 31
SP - 2087
EP - 2101
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 8
ER -