Elad Tzalik

activity

20222026

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5 papers · 1 filter

math.CO2026

The Structure of Cycles in Projective Geometry over $F_{q}$

Ran J. Tessler, Elad Tzalik

A classical geometric result says that every nonzero cycle of the mod- $2$ incidence map from $d$ -subsets to $(d - 1)$ -subsets of $[n]$ has support at least $d + 1$ , with equality attai…

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 $Ω\lef…

math.CO2023

On the Number of Shortest Paths in Graphs

Itai Benjamini, Elad Tzalik

It is proved that the number of shortest paths between two vertices of distance $t$ in a graph with degrees bounded by $Δ$ is at most $2 \cdot (\frac{Δ}{2})^{t}$ . This improves upon th…

math.CO2023

Topological expansion for posets and the homological $k$ -connectivity of random $q$ -complexes

Ran Tessler, Elad Tzalik

We study high dimensional expansion beyond simplicial complexes (posets) and focus on $q$ -complexes which are complexes whose basic building blocks are linear spaces. We show that…

math.CO2023

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 $(3^{\frac{1}{3}})^{n^{d} \pm o (n^{d})}$ .

The Structure of Cycles in Projective Geometry over Fq​

Hypercube minor-universality

On the Number of Shortest Paths in Graphs

Topological expansion for posets and the homological k-connectivity of random q-complexes

The number of tiles of Zd

The Structure of Cycles in Projective Geometry over $F_{q}$

Topological expansion for posets and the homological $k$ -connectivity of random $q$ -complexes

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