7 citations · 17 across the 8 of their papers we have counts for
9 papers
Disjoint and nearly disjoint sums of matrix multiplication tensors and their centroids
Martin Kassabov, J. M. Landsberg, Victor Souza +1
This paper addresses centroids, which are fundamental invariants of tensors. Our main results are as follows: (i) The construction of explicit tensors with very large centroids, wh…
Localised graph Maclaurin inequalities
Lucas Aragão, Victor Souza
The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Turán and Zykov. In a nutshell they provide an asymptotically sharp answer to the foll…
A note on the number of Egyptian fractions
Noah Lebowitz-Lockard, Victor Souza
Refining an estimate of Croot, Dobbs, Friedlander, Hetzel and Pappalardi, we show that for all , the number of integers such that the equation $a/n = 1/…
Expander graphs are globally synchronizing
Pedro Abdalla, Afonso S. Bandeira, Martin Kassabov +3
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively w…
Improved bounds for the dimension of divisibility
Victor Souza, Leo Versteegen
The dimension of a partially-ordered set is the smallest integer such that one can embed into a product of linear orders. We prove that the dimension of the divisib…
The Maker-Breaker percolation game on the square lattice
Vojtěch Dvořák, Adva Mond, Victor Souza
We study the Maker-Breaker percolation game on , introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the…
The order dimension of divisibility
David Lewis, Victor Souza
The Dushnik-Miller dimension of a partially-ordered set is the smallest such that one can embed into a product of linear orders. We prove that the dimension of the…
Blowup Ramsey numbers
Victor Souza
We study a generalisation of the bipartite Ramsey numbers to blowups of graphs. For a graph , denote the -blowup of by . We say that is -Ramsey for , and…
The Typical Structure of Sets with Small Sumset
Marcelo Campos, Maurício Collares, Robert Morris +2
In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we…