Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.23664

Line spreads of W(2n-1, q), q even

Daniele Bartoli·Antonio Cossidente·Giuseppe Marino·Francesco Pavese
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let q be an even prime power and n \ge 2. We construct line spreads of the symplectic polar space W(2n-1,q) by replacing pairwise disjoint reguli in a Desarguesian line spread. The construction is based on partitions of the points of PG(n-1,q^2) into points of a nondegenerate Hermitian variety and Baer sublines meeting that variety in exactly one point. In the plane case, the partition is invariant under a cyclic group of order q^2-q+ 1.

Explore related subjects

math.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daniele Bartoli, Antonio Cossidente, Giuseppe Marino, Francesco Pavese. 2026-10-16. Line spreads of W(2n-1, q), q even. https://arxiv.org/abs/2610.23664

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Observations on the hex clusters of the Spectre tilings

Decorating the Spectre tile with hexagons reveals triangular hexagonal clusters whose structure we study. In the process we reprove that the Spectre tilings exist and are uniquely hierarchical. The proof is not computer-assisted.

math.CO↗
arXiv2026

$(2k+1)$-Neighborhood Balanced Coloring

Let $G=(V,E)$ be a simple graph and $(2k+1)$ be a prime integer. Let each vertex of $G$ be colored using one of the $(2k+1)$ colors, say $R_1,R_2,...,R_{2k+1}$. If every vertex has an equal number of neighbors of each color, then the coloring is a $(2k+1)$-neighborhood balanced coloring. We establish a number of results for common families of graphs and present some families of graphs that have this property.

math.CO↗
arXiv2026

The largest sets of non-opposite chambers in spherical buildings of type $B$

The investigation into large families of non-opposite flags in finite spherical buildings has been a recent addition to a long line of research in extremal combinatorics, extending classical results in vector and polar spaces. This line of research falls under the umbrella of Erdős-Ko-Rado (EKR) problems, but poses some extra difficulty on the algebraic level compared to aforementioned classical results. From the building theory point of view, it can be seen as a variation of the center conjecture for spherical buildings due to Tits, where we replace the convexity assumption by a maximality condition. In previous work, general upper bounds on the size of families of non-opposite flags were obtained by applying eigenvalue and representation-theoretic techniques to the Iwahori-Hecke algebras of non-exceptional buildings. More recently, the classification of families reaching this upper bound in type $A_n$, for $n$ odd, was accomplished by Heering, Lansdown, and Metsch. For buildings of type $B$, the corresponding Iwahori-Hecke algebra is more complicated and depends non-trivially on the type and rank of the underlying polar space. Nevertheless, we are able to find a uniform method based on antidesigns and obtain classification results for chambers (i.e.\ maximal flags) in most cases.

math.CO↗