Sergey Avvakumov

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20242026

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math.CO2025

Tensor rank of the determinant and periodic triangulations of $R^{n}$

Sergey Avvakumov, Roman Karasev

We prove that in any $Z^{n}$ -periodic triangulation of $R^{n}$ the number of $Z^{n}$ -orbits of $n$ -dimensional simplices is at least the tensor rank of the $n$ …

math.CO2025

Cubulating the sphere with many facets

Sergey Avvakumov, Alfredo Hubard

For each $d \geq 3$ we construct cube complexes homeomorphic to the $d$ -sphere with $n$ vertices in which the number of facets (assuming $d$ constant) is $Ω (n^{5/4})$ . This disprove…

Tensor rank of the determinant and periodic triangulations of Rn

Cubulating the sphere with many facets

Tensor rank of the determinant and periodic triangulations of $R^{n}$