Pattern avoidance in ordered set partitions and words
نویسندگان
چکیده
منابع مشابه
Pattern Avoidance in Ordered Set Partitions
In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for certain special cases, and a recursive technique to exactly enumerate the appropriate set partitions in general. We also give some asymptotic results for the growth rates of the number of ordered set partitions avoiding a single pattern; includ...
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The study of patterns in permutations is a very active area of current research. Klazar defined and studied an analogous notion of pattern for set partitions. We continue this work, finding exact formulas for the number of set partitions which avoid certain specific patterns. In particular, we enumerate and characterize those partitions avoiding any partition of a 3-element set. This allows us ...
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We show structural properties of the system of ordered partitions of [n] := {1, . . . , n} all of whose left-to-right minima occur in odd locations, called left-to-right arrangements. Our main objectives are (i) to show that the set of all finite left-to-right arrangements is a projective system under a natural choice of restriction operation, (ii) to establish a non-trivial embedding of set pa...
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In 2000 Klazar introduced a new notion of pattern avoidance in the context of set partitions of [n] = {1, . . . , n}. The purpose of the present paper is to undertake a study of the concept of Wilf-equivalence based on Klazar’s notion. We determine all Wilf-equivalences for partitions with exactly two blocks, one of which is a singleton block, and we conjecture that, for n ≥ 4, these are all th...
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To atten a set partition (with apologies to Mathematica r ) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing|increasing entries in each block and blocks arranged in increasing order of their rst entries|we count the partitions of [n] whose attening avoids a single 3-letter pattern. Five coun...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2014
ISSN: 0196-8858
DOI: 10.1016/j.aam.2014.08.004