科研之友
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摘要
It is well-known that Catalan numbers C(n) = 1/n+1 ((2n)(n)) 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-Slit arrangement and partitions which are both n-cores as well as (mn + 1)-cores.
- 出版日期2010-12
