منابع مشابه
Set 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 کاملClosed 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 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 کاملPartition Statistics for Cubic Partition Pairs
In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1994
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90107-4