Counting pattern-avoiding integer partitions
نویسندگان
چکیده
منابع مشابه
On Pattern-Avoiding Partitions
A set partition of size n is a collection of disjoint blocks B1, B2, . . . , Bd whose union is the set [n] = {1, 2, . . . , n}. We choose the ordering of the blocks so that they satisfy minB1 < minB2 < · · · < minBd. We represent such a set partition by a canonical sequence π1, π2, . . . , πn, with πi = j if i ∈ Bj. We say that a partition π contains a partition σ if the canonical sequence of π...
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We identify several subsets of the partitions of [n], each characterized by the avoidance of a pair of patterns, respectively of lengths four and five. Each of the classes we consider is enumerated by the Catalan numbers. Furthermore, the members of each class having a prescribed number of blocks are enumerated by the Narayana numbers. We use both algebraic and combinatorial methods to establis...
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An ordered partition of [n] = {1, 2, . . . , n} is a partition whose blocks are endowed with a linear order. Let OPn,k be the set of ordered partitions of [n] with k blocks and OPn,k(σ) be the set of ordered partitions in OPn,k that avoid a pattern σ. For any permutation pattern σ of length three, Godbole, Goyt, Herdan and Pudwell obtained formulas for the number of ordered partitions of [n] wi...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2020
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-020-00287-6