A geometric condition for incidence-matrix nullvectors
Let (P,L) be a (point,line)-geometry, in which L is a collection of subsets of size \(s+1\) of P. Suppose there exists a function e: \(P\to {\mathbb{Z}}\) such that, for each \(p\in P\) and \(\ell \in L\), there is a unique \(q\in \ell\) such that \(e(\ell)=\{e(q),e(q)+1\}\). Then \(\sum_{p\in P}(- s)^{-e(p)}P\) lies in the kernel of the point-line incidence matrix of (P,L). Several instances of this phenomenon (notably) near polygons and an infinite cover) are discussed.
scientific article; zbMATH DE number 4110704
scientific article