منابع مشابه
On ^-derangement Numbers
We derive a (/-analogue of the classical formula for the number of derangements of an n element set. Our derivation is entirely analogous to the classical derivation, but relies on a descent set preserving bijection between the set of permutations with a given derangement part and the set of shuffles of two permutations. A classical application of binomial inversion (more generally the principl...
متن کاملLabeled Partitions and the q-Derangement Numbers
Inspired by MacMahon’s original proof of his celebrated theorem on the distribution of the major index over permutations, we give a reformulation of his argument in terms of labeled partitions. In this framework, we establish a decomposition theorem for labeled partitions which is analogous to the decomposition of a permutation into derangement points and fixed points. This decomposition implie...
متن کاملThe limiting distribution of the q-derangement numbers
We prove the normality of the limiting distribution of the coefficients of the q-derangement numbers of type B based on the formula of Foata and Han that contains a parameter z. Setting the parameter z to zero, we are led to the case of ordinary q-derangement numbers. For z = 1, we obtain the normality of the distribution of the coefficients of the usual q-derangement numbers of type B.
متن کاملThe ratio monotonicity of the q-derangement numbers
We show that the q-derangement numbers satisfy a ratio monotone property, which is analogous to the log-concavity and is stronger than the spiral property and the unimodality.
متن کاملClosed Forms for Derangement Numbers in Terms of the Hessenberg Determinants
In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00757-4