Zobrazeno 1 - 10
of 685
pro vyhledávání: '"05B15"'
Autor:
Allsop, Jack, Wanless, Ian M.
A quasigroup is a pair $(Q, *)$ where $Q$ is a non-empty set and $*$ is a binary operation on $Q$ such that for every $(a, b) \in Q^2$ there exists a unique $(x, y) \in Q^2$ such that $a*x=b=y*a$. Let $(Q, *)$ be a quasigroup. A pair $(x, y) \in Q^2$
Externí odkaz:
http://arxiv.org/abs/2412.08107
Autor:
Krotov, Denis S.
For the Hamming graph $H(n,q)$, where a $q$ is a constant prime power and $n$ grows, we construct perfect colorings without non-essential arguments such that $n$ depends exponentially on the off-diagonal part of the quotient matrix. In particular, we
Externí odkaz:
http://arxiv.org/abs/2412.04461
Autor:
Kuznetsov, Eugene
In this work, the author gives a character-free proof of the Frobenius theorem. The new proof is based on some notions and results from the theory of ternary operations, the theory of orthogonal binary operations, the theory of transversals in groups
Externí odkaz:
http://arxiv.org/abs/2412.00712
We will show that there are at least 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of orders $n=54$, $96$ and $108$. The cases $n=54$ and $96$ are obtained by constructing separable permutation codes consisting of $8 \times 54$ and $10 \times
Externí odkaz:
http://arxiv.org/abs/2412.00480
A sequence covering array, denoted \textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\{0, \dots, v-1 \}$ such that each sequence of $t$ distinct elements of $\{0, \dots, v-1\}$ reads left to right in at least one permutation. The minimum number
Externí odkaz:
http://arxiv.org/abs/2411.17145
We characterize mixed-level orthogonal arrays it terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer-Friedman (BF) bound for pure-level orthogonal arrays. For the case when the numbers of levels are pow
Externí odkaz:
http://arxiv.org/abs/2411.16559
Autor:
Flores, Daniel
We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a direct meth
Externí odkaz:
http://arxiv.org/abs/2411.01091
Autor:
Falcón, Raúl M., Mella, Lorenzo
A Heffter array over an additive group $G$ is any partially filled array $A$ satisfying that: (1) each one of its rows and columns sum to zero in $G$, and (2) if $i\in G\setminus\{0\}$, then either $i$ or $-i$ appears exactly once in $A$. In this pap
Externí odkaz:
http://arxiv.org/abs/2410.23216
The Hadamard quasigroup product has recently been introduced as a natural generalization of the classical Hadamard product of matrices. It is defined as the superposition operator of three binary operations, one of them being a quasigroup operation.
Externí odkaz:
http://arxiv.org/abs/2410.23183
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, th
Externí odkaz:
http://arxiv.org/abs/2410.09546