Restricted growth function patterns and statistics
| Autor: | Jonathan Gerhard, Bruce E. Sagan, Lindsey R. Campbell, Thomas Grubb, Carlin Purcell, Samantha Dahlberg, Robert Dorward |
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| Rok vydání: | 2016 |
| Předmět: |
Sequence
Multiset 05A15 (Primary) 05A05 05A18 05A19 (Secondary) Applied Mathematics 010102 general mathematics 0102 computer and information sciences 01 natural sciences Growth function 010201 computation theory & mathematics Statistics Bijection FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1605.04807 |
| Popis: | A restricted growth function (RGF) of length n is a sequence w = w_1 w_2 ... w_n of positive integers such that w_1 = 1 and w_i is at most 1 + max{w_1,..., w_{i-1}} for i at least 2. RGFs are of interest because they are in natural bijection with set partitions of {1, 2, ..., n}. RGF w avoids RGF v if there is no subword of w which standardizes to v. We study the generating functions sum_{w in R_n(v)} q^{st(w)} where R_n(v) is the set of RGFs of length n which avoid v and st(w) is any of the four fundamental statistics on RGFs defined by Wachs and White. These generating functions exhibit interesting connections with integer partitions and two-colored Motzkin paths, as well as noncrossing and nonnesting set partitions. Comment: 39 pages, 5 figures, added references and other material |
| Databáze: | OpenAIRE |
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