Zobrazeno 1 - 10
of 98
pro vyhledávání: '"De Beule, Jan"'
We continue our investigation of Erd\H{o}s-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the classificat
Externí odkaz:
http://arxiv.org/abs/2408.05015
This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\mathrm{PG}(n,q)$ or $\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size of this co
Externí odkaz:
http://arxiv.org/abs/2403.00519
Publikováno v:
Finite Fields and Their Applications Volume 95, 102387 (2024)
In this paper, we provide a construction of $(q+1)$-ovoids of the hyperbolic quadric $Q^+(7,q)$, $q$ an odd prime power, by glueing $(q+1)/2$-ovoids of the elliptic quadric $Q^-(5,q)$. This is possible by controlling some intersection properties of (
Externí odkaz:
http://arxiv.org/abs/2307.03542
Publikováno v:
European Journal of Combinatorics (2024)
In this paper we develop non-existence results for $m$-ovoids in the classical polar spaces $Q^-(2r+1,q), W(2r-1,q)$ and $H(2r,q^2)$ for $r>2$. In [4] a lower bound on $m$ for the existence of $m$-ovoids of $H(4,q^2)$ is found by using the connection
Externí odkaz:
http://arxiv.org/abs/2305.06285
In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces ${\cal W}(3, q)$, $q$ odd square, $q \not\equiv 0 \pmod{3}$, ${\cal W}(5, q)$ and of the Hermitian polar spaces ${\cal H}(4,
Externí odkaz:
http://arxiv.org/abs/2203.04553
We investigate the existence of Boolean degree $d$ functions on the Grassmann graph of $k$-spaces in the vector space $\mathbb{F}_q^n$. For $d=1$ several non-existence and classification results are known, and no non-trivial examples are known for $n
Externí odkaz:
http://arxiv.org/abs/2202.03940
A modular equality for Cameron-Liebler line classes in projective and affine spaces of odd dimension
Autor:
De Beule, Jan, Mannaert, Jonathan
Publikováno v:
Finite Fields and Their Applications, Volume 82, 102047 (2022)
In this article we study Cameron-Liebler line classes in PG$(n,q)$ and AG$(n,q)$, objects also known as boolean degree one functions. A Cameron-Liebler line class $\mathcal{L}$ is known to have a parameter $x$ that depends on the size of $\mathcal{L}
Externí odkaz:
http://arxiv.org/abs/2110.09330
Publikováno v:
Designs, Codes and Cryptography, 2022
In this article we generalize the concepts that were used in the PhD thesis of Drudge to classify Cameron-Liebler line classes in PG$(n,q), n\geq 3$, to Cameron-Liebler sets of $k$-spaces in PG$(n,q)$ and AG$(n,q)$. In his PhD thesis, Drudge proved t
Externí odkaz:
http://arxiv.org/abs/2106.05684
Publikováno v:
In European Journal of Combinatorics May 2024 118
Publikováno v:
In Finite Fields and Their Applications March 2024 95