Henri Mühle and Christian Krattenthaler

The rank enumeration of certain parabolic non-crossing partitions

(31 pages)

Abstract. We consider m-divisible non-crossing partitions of {1,2,...,mn} with the property that for some t <= n no block contains more than one of the first t integers. We give a closed formula for the number of multi-chains of such non-crossing partitions with prescribed number of blocks. Building on this result, we compute Chapoton's M-triangle in this setting and conjecture a combinatorial interpretation for the H-triangle. This conjecture is proved for m=1.

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