Related papers: On irreducible meanders growth rate
In this article we obtain an improved upper bound for the regularity of binomial edge ideals of trees.
We solve a problem due to Recam\'an about the lower bound behavior of the maximum possible length among all arithmetic progressions in the least reduced residue system modulo $n$, as $n \to \infty$.
We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.
It is shown that a band-limited function bounded by 1 for negative x can grow arbitrarily fast for positive x.
We present upper and two-sided bounds of the exponential growth rate for a wide range of power-free languages. All bounds are obtained with the use of algorithms previously developed by the author.
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s=(s1,s2) we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be…
In a recent paper, Bary-Soroker, Koukoulopoulos and Kozma proved that when $A$ is a random monic polynomial of $\mathbb{Z}[X]$ of deterministic degree $n$ with coefficients $a_j$ drawn independently according to measures $\mu_j,$ then $A$…
We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for lattices. This article is mainly based on a part of the author's…
A partition into distinct parts is refinable if one of its parts $a$ can be replaced by two different integers which do not belong to the partition and whose sum is $a$, and it is unrefinable otherwise. Clearly, the condition of being…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
Here, we give upper and lower bounds on the count of positive integers $n\le x$ dividing the $n$th term of a nondegenerate linearly recurrent sequence with simple roots.
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…
Let $U_n(q)$ be the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. In this paper, we present constructions of large degree ordinary irreducible representations of $U_n(q)$ where $n\geq 7$, and then…
A general achievable upper bound of extractable work under feedback control is given, where nonequilibrium equalities are generalized so as to be applicable to error-free measurements. The upper bound involves a term which arises from the…
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…