Alexander L. Gavrilyuk

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20192026

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math.CO2026

Intersecting Families of Spanning Trees of $K_{n, n}$

Gordian C. Bruns, Dheer Noal Desai, Alexander L. Gavrilyuk +2

A family of spanning trees of a graph is $t$ -intersecting if any pair of spanning trees in the family has $t$ or more edges in common. For sufficiently large $n$ and $t \leq n/C\lo…

math.CO2021

A modular equality for $m$ -ovoids of elliptic quadrics

Alexander L. Gavrilyuk, Klaus Metsch, Francesco Pavese

An $m$ -ovoid of a finite polar space $P$ is a set $O$ of points such that every maximal subspace of $P$ contains exactly $m$ points of $O$ .…

math.CO2019

On tight sets of hyperbolic quadrics

Alexander L. Gavrilyuk

We prove that the parameter $x$ of a tight set $T$ of a hyperbolic quadric $Q^{+} (2 n + 1, q)$ of an odd rank $n + 1$ satisfies $(2 x) + w (w - x) \equiv 0 mod q + 1$ , wh…

Intersecting Families of Spanning Trees of Kn,n​

A modular equality for m-ovoids of elliptic quadrics

On tight sets of hyperbolic quadrics

Intersecting Families of Spanning Trees of $K_{n, n}$

A modular equality for $m$ -ovoids of elliptic quadrics