منابع مشابه
Actions and Identities on Set Partitions
A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of An on the set of A-labeled partitions of an (n + 1)-set. By investigating the orbit decomposition of various families of set partitions under th...
متن کاملGroup Actions on Partitions
We introduce group actions on the integer partitions and their variances. Using generating functions and Burnside’s lemma, we study arithmetic properties of the counting functions arising from group actions. In particular, we find a modulo 4 congruence involving the number of ordinary partitions and the number of partitions into distinct parts.
متن کاملPolynomial identities for partitions
For any partition λ of an integer n , we write λ =< 11, 22, . . . , nn > where mi(λ) is the number of parts equal to i . We denote by r(λ) the number of parts of λ (i.e. r(λ) = ∑n i=1mi(λ) ). Recall that the notation λ ` n means that λ is a partition of n . For 1 ≤ k ≤ N , let ek be the k-th elementary symmetric function in the variables x1, . . . , xN , let hk be the sum of all monomials of to...
متن کاملOn the identities of modulo-p partitions
Some identities between partitions and compositions were obtained in the literature. As a natural extension, we introduce and study modulo-p partitions, where p is a positive integer. Moreover, several recurrence relations and some sufficient conditions for the existence of modulo-p partitions are given, respectively. In addition, we obtain some identities of modulo-p partitions. In the end, us...
متن کاملSome Bijections on Set Partitions
We study three similar bijections on set partitions. The first is an involution defined by Kasraoui and Zeng which proves the symmetry of the distribution of crossings and nestings. We show that a stronger result can be deduced. The second gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution. The third proves the equivalence of a multivariate block size di...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/1992