Sven C. Polak

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3 papers · 1 filter

math.CO2026

Lean-verified lower bounds for the Shannon capacity of odd cycles

Pjotr Buys, Sven Polak, Jeroen Zuiddam

We give new lower bounds for the Shannon capacities of small odd cycles: $Θ (C_{7}) \geq 3.258805369885 \dots$ , $Θ (C_{11}) \geq 5.294502522149 \dots$ , $Θ (C_{13}) \geq 6.302455083464 \dots$ ,…

math.CO2025

A group-theoretic approach to Shannon capacity of graphs and a limit theorem from lattice packings

Pjotr Buys, Sven Polak, Jeroen Zuiddam

We develop a group-theoretic approach to the Shannon capacity problem. Using this approach we extend and recover, in a structured and unified manner, various families of previously…

math.CO2025

Semidefinite lower bounds for covering codes

Dion Gijswijt, Sven Polak

Let $K_{q} (n, r)$ denote the minimum size of a $q$ -ary covering code of word length $n$ and covering radius $r$ . In other words, $K_{q} (n, r)$ is the minimum size of a set of $q$ -ary cod…