Zobrazeno 1 - 10
of 264
pro vyhledávání: '"51E15"'
Autor:
Adriaensen, Sam, Weiner, Zsuzsa
The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kiss and Somlai recently proved interesting properties of the set of poin
Externí odkaz:
http://arxiv.org/abs/2411.19202
The function $p_{xy}$ that interchanges two logical variables $x,y$ in formulas is hard to describe in the following sense. Let $F$ denote the Lindenbaum-Tarski formula-algebra of a finite-variable first order logic, endowed with $p_{xy}$ as a unary
Externí odkaz:
http://arxiv.org/abs/2409.04088
We present various new constructions and bounds for arcs in projective Hjelmslev planes over finite chain rings of nilpotency index 2. For the chain rings of cardinality at most 25 we give updated tables with the best known upper and lower bounds for
Externí odkaz:
http://arxiv.org/abs/2409.02099
Autor:
Kantor, William M.
Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag $(\infty,
Externí odkaz:
http://arxiv.org/abs/2408.11923
Autor:
Coulter, Robert, Senger, Steven
In a previous article, the authors determined the first (and at the time of writing, the only) non-trivial upper bound for the cardinality of the image set for several classes of functions, including planar functions. Here, we show that the upper bou
Externí odkaz:
http://arxiv.org/abs/2406.03655
The classification of the $2$-designs with $\lambda=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by using conics and hyperovals of $PG(2,q)
Externí odkaz:
http://arxiv.org/abs/2404.19190
Autor:
Asgarli, Shamil, Yip, Chi Hoi
Given two irreducible conics $C$ and $D$ over a finite field $\mathbb{F}_q$ with $q$ odd, we show that there are $q^2/4+O(q^{3/2})$ points $P$ in $\mathbb{P}^2(\mathbb{F}_q)$ such that $P$ is external to $C$ and internal to $D$. This answers a questi
Externí odkaz:
http://arxiv.org/abs/2404.06754
A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $\lambda$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, \lambda)$ if has the smallest p
Externí odkaz:
http://arxiv.org/abs/2401.15411
Autor:
Araujo-Pardo, Gabriela, Conder, Marston, García-Colín, Natalia, Kiss, György, Leemans, Dimitri
In this paper, we introduce a problem closely related to the Cage Problem and the Degree Diameter Problem. For integers $k\geq 2$, $g\geq 3$ and $d\geq 1$, we define a $(k;\, g,d)$-graph to be a $k$-regular graph with girth $g$ and diameter $d$. We d
Externí odkaz:
http://arxiv.org/abs/2401.15539
In order to reprove an old result of R\'edei's on the number of directions determined by a set of cardinality $p$ in $\mathbb{F}_p^2$, Somlai proved that the non-constant polynomials over the field $\mathbb{F}_p$ whose range sums are equal to $p$ are
Externí odkaz:
http://arxiv.org/abs/2311.06136