منابع مشابه
Closed Expressions for Averages of Set Partition Statistics
In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field we found that the moments (mean, variance and higher moments) of novel statistics on set partitions of [n] = {1, 2, · · · , n} have simple closed expressions as linear combinations of shifted bell numbers. It is shown here that families of other statistics have similar moments. T...
متن کاملSet partition patterns and statistics
A set partition σ of [n] = {1, . . . , n} contains another set partition π if restricting σ to some S ⊆ [n] and then standardizing the result gives π. Otherwise we say σ avoids π. For all sets of patterns consisting of partitions of [3], the sizes of the avoidance classes were determined by Sagan and by Goyt. Set partitions are in bijection with restricted growth functions (RGFs) for which Wach...
متن کاملSet partition statistics and q-Fibonacci numbers
We consider the set partition statistics ls and rb introduced by Wachs and White and investigate their distribution over set partitions avoiding certain patterns. In particular, we consider those set partitions avoiding the pattern 13/2, Πn(13/2), and those avoiding both 13/2 and 123, Πn(13/2, 123). We show that the distribution over Πn(13/2) enumerates certain integer partitions, and the distr...
متن کاملCentral Limit Theorems for Some Set Partition Statistics
We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1, 2, . . . , n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels.
متن کاملExplicit expressions for the extremal excedance set statistics
Abstract The excedance set of a permutation π = π1π2 · · ·πk is the set of indices i for which πi > i. We give explicit formulas for the number of permutations whose excedance set is the initial segment {1, 2, . . . ,m} and also of the form {1, 2, . . . ,m,m + 2}. We provide two proofs. The first is an explicit combinatorial argument using rook placements. The second uses the chromatic polynomi...
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ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2014
ISSN: 2197-9847
DOI: 10.1186/2197-9847-1-2