Yair Lavi

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math.CO2026

A linear gap for the maximal cp-rank

Yair Lavi

We prove that the maximal cp-rank $p_{n}$ satisfies $p_{n} \geq n (n - 3) /2$ for odd $n \geq 5$ and $p_{n} \geq n (n - 3) /2 - 1$ for even $n \geq 6$ . Together with the known upper bound $p_n\le\binom{n+1}…

math.CO2026

The Wang Transform Inequality

Yair Lavi

We prove the Wang transform inequality in every order: if $n$ is a positive integer, $A$ is a nonnegative $n \times n$ matrix whose row and column sums equal one, and $J_{n}$ has ever…

math.CO2026

The Marcus-Minc Transform Inequality

Yair Lavi

We prove the Marcus-Minc conjecture: let n be any integer at least 2, and let A be a nonnegative n by n matrix whose row and column sums are all one. Form a new matrix by subtracti…

math.CO2026

The Maximum Permanent of a Stochastic Matrix of Bounded Rank

Yair Lavi

Let $A$ be a stochastic $n \times n$ matrix with $rank A \leq k$ , where $1 \leq k \leq n$ . Write $n = q k + s$ , where $0 \leq s < k$ . The author conjectured in 2018 that $\operat…

math.CO2026

A counterexample to the Foregger-Sinkhorn tie-point conjecture

Yair Lavi

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 prescr…

math.CO2026

The Maximum of $per (I - A)$ in Odd Order

Yair Lavi

Let $Ω_{n}$ denote the set of $n \times n$ doubly stochastic matrices. Kim and Roush conjectured in 1981 that, for $n = 2 k + 1 > 1$ , $ \max_{A\inΩ_{2k+1}}\operatorname{per}(I-A)=3\cdot 2^{k…

A linear gap for the maximal cp-rank

The Wang Transform Inequality

The Marcus-Minc Transform Inequality

The Maximum Permanent of a Stochastic Matrix of Bounded Rank

A counterexample to the Foregger-Sinkhorn tie-point conjecture

The Maximum of per(I−A) in Odd Order

The Maximum of $per (I - A)$ in Odd Order