منابع مشابه
A maj Statistic for Set Partitions
We propose a weighting of set partitions which is analogous to the major index for permutations. The corresponding weight generating function yields the q-Stirling numbers of the second kind of Carlitz and Gould. Other interpretations of maj are given in terms of restricted growth functions, rook placements and reduced matrices. The Foata bijection interchanging inv and maj for permutations als...
متن کاملA Spatial Scan Statistic for Stochastic Scan Partitions
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متن کاملA Gray Code for Set Partitions
We consider here the collection of all partitions of an n-set, for fixed n, and we ask: is it possible to arrange these partitions in a list (Gray Code) so that each partition is obtained from its immediate predecessor by changing the class of exactly one element? The answer is affirmative, and we give descriptions of two algorithms which implement the method, the first recursive, the second no...
متن کاملA Multi-set Identity for Partitions
Amitai REGEV 1 and Doron ZEILBERGER Added Sept. 22, 2009 Guo-Niu Han kindly pointed out to us (something that we should have noticed ourselves if we would have been in the habit of reading carefully all the papers that we cite), that our main result is contained in [B.H.]. Introduction Given an integer-partition λ ` n and a box (a cell) v = [i, j] ∈ λ it determines the arm length av (= λi − j),...
متن کاملSet Partitions in R
This short paper introduces a code snippet in the form of an R function that enumerates all possible partitions of a finite set given the sizes of the equivalence classes. Three combinatorial problems are solved using the software: one from bioinformatics, one from scheduling theory, and one from forensic science.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1991
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(13)80009-1