Related papers: Upper bounds on Kronecker coefficients with few ro…
We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the…
The computation of Kronecker coefficients is a challenging problem with a variety of applications. In this paper we present an approach based on methods from symplectic geometry and residue calculus. We outline a general algorithm for the…
For relatively prime positive integers $u_0$ and $r$ and for $0\le k\le n$, define $u_k:=u_0+kr$. Let $L_n:={\rm lcm}(u_0, u_1, ..., u_n)$ and let $a, l\ge 2$ be any integers. In this paper, we show that, for integers $\alpha \geq a$ and…
We obtain some new upper bounds on the Ramsey numbers of the form $R(\underbrace{C_4,\ldots,C_4}_m,G_1,\ldots,G_n)$, where $m\ge 1$ and $G_1,\ldots,G_n$ are arbitrary graphs. We focus on the cases of $G_i$'s being complete, star $K_{1,k}$…
We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the…
Problem of finding an optimal upper bound for {\chi} of (3 Times K1)-free graphs is still open and pretty hard. It was proved by Choudum et al that upper bound on the {\chi} of {3 Times K1, {2 Times K1 + (K2 UNION K1)}-free graphs is…
Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor distances have been established for the Euclidean and the maximum…
The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded $k$-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several…
We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok and Gurvits. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes.…
We prove that each eigenvalue l(k) of the Kirchhoff Laplacian K of a graph or quiver is bounded above by d(k)+d(k-1) for all k in {1,...,n}. Here l(1),...,l(n) is a non-decreasing list of the eigenvalues of K and d(1),..,d(n) is a…
We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker…
The stretched Littlewood-Richardson coefficient $c^{t\nu}_{t\lambda,t\mu}$ was conjectured by King, Tollu, and Toumazet to be a polynomial function in $t.$ It was shown to be true by Derksen and Weyman using semi-invariants of quivers.…
We prove Gaussian upper and lower bounds for the fundamental solutions of a class of degenerate parabolic equations satisfying a weak Hormander condition. The bound is independent of the smoothness of the coefficients and generalizes…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the special case of Kostka numbers.
We suggest an upper bound on binomial coefficients that holds over the entire parameter range and whose form repeats the form of the de Moivre-Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the…
The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital angular momentum number l…
Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). We describe a…
In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the diagonal Ramsey numbers since 1935. We shorten their proof, replacing the underlying book algorithm…
Newell-Littlewood coefficients $n_{\mu,\nu}^{\lambda}$ are the multiplicities occurring in the decomposition of products of universal characters of the orthogonal and symplectic groups. They may also be expressed, or even defined directly…