Related papers: On multiplicative properties of combinatorial cube…
Multiple analogues of certain families of combinatorial numbers are recently constructed by the author in terms of well poised Macdonald functions, and some of their fundamental properties are developed. In this paper, we present…
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove that for a…
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…
Bourgain, Konyagin and Shparlinski obtained a lower bound for the size of the product set AB when A and B are sets of positive rational numbers with numerator and denominator less or equal than Q. We extend and slightly improve that lower…
In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the TPP subgroup capacity of a finite group
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
We find some general lower bounds of the sum of certain families of multigraded Betti numbers of any simplicial complex with a vertex coloring.
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…
We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.
We consider the possible sizes of large sumfree sets contained in the discrete hypercube $\{1,...,n\}^k$, and we determine upper and lower bounds for the maximal size as $n$ becomes large. We also discuss a continuous analogue in which our…
We study mixed unitary quantum channels generated by irreducible projective unitary representations of finite groups. Under some assumptions on the probability distribution determining a mixture the classical capacity of the channel is…
In this paper, we study additional aspects of the capacity distribution on the set $\mathcal{B}_n$ of compositions of $n$ consisting of $1$'s and $2$'s. Among our results are further recurrences for this distribution as well as formulas for…
In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…
We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field…
We investigate the structure of two-dimensional partial cubes, i.e., of isometric subgraphs of hypercubes whose vertex set defines a set family of VC-dimension at most 2. Equivalently, those are the partial cubes which are not contractible…
Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
Three combinatorial matrices are considered and their LU-decompositions were found. This is typically done by (creative) guessing, and necessary proofs are more or less routine calculations.