Author

Yair Lavi

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Preprint Aug 2026

The Maximum Permanent of a Stochastic Matrix of Bounded Rank

Let $A$ be a stochastic $n\times n$ matrix with $\operatorname{rank}A\leq k$, where $1\leq k\leq n$. Write $n=qk+s$, where $0\leq s<k$. The author conjectured in 2018 that $\operatorname{per}A\leq (q!/q^q)^{k-s}((q+1)!/(q+1)^{q+1})^s$, with equality if and only if $A=P(J_q^{\oplus(k-s)}\oplus J_{q+1}^{\oplus s})Q$, whe...

Yair Lavi · 0 citations

Preprint Aug 2026

The Maximum of $\operatorname{per}(I-A)$ in Odd Order

Let $\Omega_n$ denote the set of $n\times n$ doubly stochastic matrices. Kim and Roush conjectured in 1981 that, for $n=2k+1>1$, $ \max_{A\in\Omega_{2k+1}}\operatorname{per}(I-A)=3\cdot 2^{k-2}$. They proposed the block construction $A_\star=\frac12(J_3-I_3)\oplus P_2^{\oplus(k-1)}$, where $P_2=\begin{pmatrix}0&1\\1&0\...

Yair Lavi · 0 citations