I. Benjamini

activity

20242026

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5 papers · 1 filter

math.CO2026

The number of tiles of $Z^{d}$

Itai Benjamini, Gady Kozma, Elad Tzalik

It is proved that the number of subsets of $[n]^{d}$ that tile $Z^{d}$ is $(3^{\frac{1}{3}})^{n^{d} \pm o (n^{d})}$ .

math.CO2025

Sums along the edges of bounded degree graphs

Noga Alon, Itai Benjamini, Georgii Zakharov +1

Let $G$ be a graph on $n$ vertices and $(H, +)$ be an abelian group. What is the minimum size $S_{H} (G)$ of the set of all sums $A (u) + A (v)$ over all injections $A : V (G) \to H$ ? In…

math.CO2025

A very sharp threshold for first order logic distinguishability of random graphs

Itai Benjamini, Maksim Zhukovskii

In this paper we find an integer $h = h (n)$ such that the minimum number of variables of a first order sentence that distinguishes between two independent uniformly distributed rando…

math.CO2025

Majority dynamics on finite trees

Itai Benjamini, Georgii Zakharov, Maksim Zhukovskii

For an arbitrary finite tree $T$ , we find the exact value of the wort-case stabilisation time of majority dynamics on $T$ . We also prove that for a perfect rooted cubic tree $T$ wi…

math.CO2025

Hypercube minor-universality

Itai Benjamini, Or Kalifa, Elad Tzalik

A graph $G$ is $m$ -minor-universal if every graph with at most $m$ edges (and no isolated vertices) is a minor of $G$ . We prove that the $d$ -dimensional hypercube, $Q_{d}$ , is $Î©\le…

The number of tiles of Zd

Sums along the edges of bounded degree graphs

A very sharp threshold for first order logic distinguishability of random graphs

Majority dynamics on finite trees

Hypercube minor-universality

The number of tiles of $Z^{d}$