Author

T. Prellberg

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Preprint Sep 2026

Cayley-graph density of Thompson's group F: local deletions and finite-window bounds

Let $\Gamma$ be the Cayley graph of Thompson's group $F$ with its standard generators. Belk and Brown constructed finite marked-forest subgraphs of limiting density $7/2$, and Guba showed that deleting certain low-degree vertices gives density greater than $3.5004$. We refine this approach in two directions. First, a d...

T. Prellberg · 0 citations

Preprint Sep 2026

Moment obstructions and continuum-to-discrete bounds for checkerboard no-three-in-line sets

Fix one colour class in the checkerboard colouring of an $n\times n$ integer grid, and let $M_4(n,\varepsilon)$ be the largest subset having at most two points in every row, column, and diagonal of slopes $\pm1$. We prove the near-saturation bound $M_4(n,\varepsilon)\leq2n-4$ for $n\geq6$. The proof uses first and seco...

Jujhar Aujla, T. Prellberg, Nirvair Sandhu · 1 citation