Enumeration of non-crossing partitions according to subwords with repeated letters
Abstract
An avoidance pattern where the letters within an occurrence of which are required to be adjacent is referred to as a subword. In this paper, we enumerate members of the set NC_n of non-crossing partitions of length n according to the number of occurrences of several infinite families of subword patterns each containing repeated letters. As a consequence of our results, we obtain explicit generating function formulas counting the members of NC_n for n >= 0 according to all subword patterns of length three containing a repeated letter. Further, simple expressions are deduced for the total number of occurrences over all members of NC_n for the various families of patterns. Finally, combinatorial proofs can be given explaining three infinite families of subword equivalences over NC_n, which generalize the following equivalences: 211 = 221, 1211 = 1121 and 112 = 122.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2023
- DOI:
- 10.48550/arXiv.2303.06300
- arXiv:
- arXiv:2303.06300
- Bibcode:
- 2023arXiv230306300S
- Keywords:
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- Mathematics - Combinatorics;
- 05A15