Mathematics · science · research
Hello, and welcome. Here I collect and share my research in mathematics, which has always been a great passion of mine. I use AI to explore my favorite topics and have managed to resolve several open questions, including a conjecture of my own. By day, I serve as Head of AI and Algorithms in Israel’s high-tech sector. Outside work and mathematics, I enjoy playing chess. For updates on the Minc’s list project, see here.
Research interests Combinatorics · Matrix theory · Representation theory · High-energy physics
Selected work
Ordered by original publication or posting date.
A quadratic permanent inequality for positive semidefinite matrices, proved through order five, with the order-four case of Soules’ permanent-on-top conjecture settled.
A proof of Wang’s 1977 conjecture that per A ≥ per((nJₙ + A)/(n + 1)) for every doubly stochastic A, with equality only at Jₙ.
A proof of the 1967 Marcus–Minc conjecture that per A ≥ per((nJₙ − A)/(n − 1)) for every doubly stochastic A, with all equality cases.
A uniform exponential lower bound for permanents of 6-regular circulant matrices that beats the general constant 3125/1296, and the optimal constant, resolving the circulant question in Minc’s Problem 10.
A proof of my 2018 conjecture giving the sharp maximum permanent of a stochastic matrix of bounded rank, with all equality cases.
The Foregger-Sinkhorn tie-point conjecture asserts that if a nearly decomposable doubly stochastic matrix minimizes the permanent on a face and the permanental cofactor at a prescribed zero is larger than its permanent, then that zero is a tie point. We give a counterexample in dimension eight.
A proof of the 1981 Kim–Roush conjecture for the maximum of per(I − A) in odd order, with a classification of all maximizers.
Two conjectures on sharp permanent and diagonal-product bounds for stochastic matrices of bounded rank.