Related papers: Combinatorics of partial wreath power of finite in…

We obtain several combinatorial results about chains, cycles and orbits of the elements of the symmetric inverse semigroup $\IS_n$ and the set $T_n$ of nilpotent elements in $\IS_n$. We also get some estimates for the growth of $|\IS_n|$…

We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of partial wreath product of inverse semigroups. As a corollary, we get the description of $\mathcal{R}$- and $\mathcal{L}$-cross-sections of the semigroupof partial automorphisms…

Let ${\cal I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2, \ldots , n\}$ and let ${\cal DDP}_n$ and ${\cal ODDP}_n$ be its subsemigroups of order-decreasing partial isometries and of order-preserving and order-decreasing partial…

We give an efficient algorithm for the enumeration up to isomorphism of the inverse semigroups of order n, and we count the number S(n) of inverse semigroups of order n<=15. This improves considerably on the previous highest-known value…

We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of wreath products of finite inverse symmetric semigroups $\mathcal{IS}_m \wr_p \mathcal{IS}_n$ up to isomorphism. We show that every isomorphism of $\mathcal{R}$ ($\mathcal{L}$-)…

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

In this paper we compute powers in the wreath product $G\wr S_n$, for any finite group $G$. For $r\geq 2$, a prime, consider $\omega_r: G\wr S_n\to G\wr S_n$ defined by $g \mapsto g^r$. Let $P_{r}(G\wr S_n)=\frac{|\omega_r(G\wr S_n)|}{|G|^n…

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories…

We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their…

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…

A small part of real line which is very close to zero has rich combinatorial properties. The aim of this paper is to express and then prove some locally combinatorial concepts near a virtual idempotent by considering the…

We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of…

Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that is by consecutive evaluations of a rational function with…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the…

Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.

We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…

We investigate the combinatorics of the general formulas for the powers of the operator $h \partial^k$, where $h$ is a central element of a ring and $\partial$ is a differential operator. This generalizes previous work on the powers of…

In this paper we deal with the problem of computing the sum of the $k$-th powers of all the elements of the matrix ring $\mathbb{M}_d(R)$ with $d>1$ and $R$ a finite commutative ring. We completely solve the problem in the case…

In this paper, we study the subconstituent algebras, also called as Terwilliger algebras, of association schemes that are obtained as the wreath product of one-class association schemes $K_n=H(1, n)$ for $n\ge 2$. We find that the $d$-class…