Related papers: Maximal Border Subrank Tensors
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
We give an exponential lower bound for Berge-Ramsey problems.
We prove a result on lower bounds in large dimensions.
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the minimal size of a decomposition of a code into rank-one…
We give general lower bounds on the maximal determinant of n by n {+1,-1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain…
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's laser method and obtain an upper bound $2.431$ on $\omega$. We also…
An upper bound of composition series of groups of finite order is obtained. The bound is a nontrivial bound and so far best possible.
We obtain lower bounds for the maximum dimension of a simple FG-module, where G is a finite group and F is an algebraically closed field of characteristic p. The bounds are described in terms of properties of p-subgroups of G. When p is 2…
Lower bounds for some explicit decision problems over the complex numbers are given.
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
Let M_n denote the matrix multiplication tensor for nxn matrices. We use the border substitution method combined with Koszul flattenings to prove the border rank lower bound of 2n^2-log(n)-1 for M_n.
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for them are proved.
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…
An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…
We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.
A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank theory. We call this property the max-full-rank-submatrix…
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
Let $M_{\langle u,v,w\rangle}\in C^{uv}\otimes C^{vw}\otimes C^{wu}$ denote the matrix multiplication tensor (and write $M_n=M_{\langle n,n,n\rangle}$) and let $det_3\in ( C^9)^{\otimes 3}$ denote the determinant polynomial considered as a…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…