arXiv subjects

Alex Cohen

Publications and source records attributed to Alex Cohen.

20 records · Page 2Linked to original sources

arXiv2020

A Sylvester-Gallai result for concurrent lines in the complex plane

We show that if a set of points in $\mathbb{C}^2$ lies on a family of $m$ concurrent lines, and if one of those lines contains more than $m-2$ points, then there is a line passing through exactly two points of the set. The bound $m-2$ in our result is optimal. Our main theorem resolves a conjecture of Frank de Zeeuw, and generalizes a result of Kelly and Nwankpa.

math.CO↗

arXiv2019

Sinkhorn limits in finitely many steps

Applied to a nonnegative $m\times n$ matrix with a nonzero $σ$-diagonal, the sequence of matrices constructed by alternate row and column scaling conveges to a doubly stochastic matrix. It is proved that if this sequence converges after only a finite number of scalings, then it converges after at most two scalings.

math.CO↗