کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4655351 | 1343380 | 2014 | 14 صفحه PDF | دانلود رایگان |
The action of the symmetric group SnSn on the set ParknParkn of parking functions of size n has received a great deal of attention in algebraic combinatorics. We prove that the action of SnSn on ParknParkn extends to an action of Sn+1Sn+1. More precisely, we construct a graded Sn+1Sn+1-module VnVn such that the restriction of VnVn to SnSn is isomorphic to ParknParkn. We describe the SnSn-Frobenius characters of the module VnVn in all degrees and describe the Sn+1Sn+1-Frobenius characters of VnVn in extreme degrees. We give a bivariate generalization Vn(ℓ,m) of our module VnVn whose representation theory is governed by a bivariate generalization of Dyck paths. A Fuss generalization of our results is a special case of this bivariate generalization.
Journal: Journal of Combinatorial Theory, Series A - Volume 123, Issue 1, April 2014, Pages 43–56