Sven C. Polak

collaborators

5 papers

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: $I^ (C_{7}) \geq 3.258805369885 \dots$ , $I^ (C_{11}) \geq 5.294502522149 \dots$ , $Î(C_{13})\geq6.302455083464\ldot…

math.CO2026

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…

math.OC2026

Sum-of-squares certificates for symmetric polynomials on the hypercube: a counterexample to a conjecture of De Klerk and Laurent

Sven Polak

This paper studies sum-of-squares (SoS) representations of nonnegative polynomials over the hypercube $[0, 1]^{n}$ . De Klerk and Laurent (SIAM J. Optim., 2010) conjectured that the sm…

cs.IT2026

Semidefinite and linear programming bounds for sum-rank-metric codes and non-existence results

Aida Abiad, Antonina P. Khramova, Sven C. Polak +1

The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distrib…

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…