Combinatorial statistics on non-crossing partitions
نویسندگان
چکیده
منابع مشابه
Combinatorial Statistics on Non-crossing Partitions
Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...
متن کاملTwo Statistics Linking Dyck Paths and Non-crossing Partitions
We introduce a pair of statistics, maj and sh, on Dyck paths and show that they are equidistributed. Then we prove that this maj is equivalent to the statistics ls and rb on non-crossing partitions. Based on non-crossing partitions, we give the most obvious q-analogue of the Narayana numbers and the Catalan numbers.
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We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restriction of having a number of blocks given. Furthermore, we generalize to k-divisible partitions. In particular, we find that in average the number of blocks of a k-divisible non-crossing partitions of nk elements is k...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1994
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90066-3