相关论文: Statistics on Wreath Products
Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.
We consider the joint distribution of the area and perimeter statistics on the set I_n of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…
Closed-form expressions for the distributions of the order statistics on the spacings between order statistics for the uniform distribution are obtained. This generalizes a result by Fisher concerning tests of significance in the harmonic…
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating function of the objects having fixed mex. We then study this…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
We calculate the exact values of the F{\o}lner function $\mathrm{F{\o}l}$ of the lamplighter group $\mathbb{Z}\wr\mathbb{Z}/2\mathbb{Z}$ for the standard generating set. More generally, for any finite group $D$ and $n\geq|D|$, we obtain the…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
We present an approach to generalised fermionic statistics which relates the existence of a generalised statistical behaviour to non-invariant ground states. Considering the thermal average of an operatorial generalization of the Heisenberg…
We prove that the pair of statistics (des,maj) on multiset permutations is equidistributed with the pair (stc,inv) on certain quotients of the symmetric group. We define the analogue of the statistic stc on multiset permutations, whose…
We study the homological finiteness property FPm of permutational wreath products.
We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of…
Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies. The current paper finds such…
We introduce the notion of crossings and nestings of a permutation. We compute the generating function of permutations with a fixed number of weak exceedances, crossings and nestings. We link alignments and permutation patterns to these…
We study the distribution of the major index with sign on some parabolic quotients of the symmetric group, extending and generalizing simultaneously results Gessel-Simion and Adin-Gessel-Roichman, and on some special trees that we call…