arXiv subjects
Publications and source records attributed to Jan-Hendrik de Wiljes.
We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $area(Δ) + area(Δ^*) = 6$ for reflexive $Δ$. The identity is equivalent to the stringy Libgober-Wood identity for toric log del Pezzo surfaces.
The coprime hypergraph of integers on $n$ vertices $CHI_k(n)$ is defined via vertex set $\{1,2,\dots,n\}$ and hyperedge set $\{\{v_1,v_2,\dots,v_{k+1}\}\subseteq\{1,2,\dots,n\}:\gcd(v_1,v_2,\dots,v_{k+1})=1\}$. In this article we present ideas on how to construct maximal subgraphs in $CHI_k(n)$. This continues the author's earlier work, which dealt with bounds on the size and structural properties of these subgraphs. We succeed in the cases $k\in\{1,2,3\}$ and give promising ideas for $k\geq 4$.