Pjotr Buys

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

The asymptotic spectrum distance, graph limits, and the Shannon capacity

David de Boer, Pjotr Buys, Jeroen Zuiddam

Determining the Shannon capacity of graphs is a long-standing open problem in information theory, graph theory and combinatorial optimization. Over decades, a wide range of upper a…

math.CO2026

Density of reliability roots of simple graphs in the unit disk

Pjotr Buys

Brown and Colbourn (1992) showed that the complex roots of the reliability polynomial of connected multigraphs are dense in the unit disk and that the closure of the real roots is…

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

Triangle-free graphs with the fewest independent sets

Pjotr Buys, Jan van den Heuvel, Ross J. Kang

Given $d > 0$ and a positive integer $n$ , let $G$ be a triangle-free graph on $n$ vertices with average degree $d$ . With an elegant induction, Shearer (1983) tightened a seminal resu…