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pro vyhledávání: '"Cavenagh, Nicholas J."'
A $\delta$-colouring of the point set of a block design is said to be {\em weak} if no block is monochromatic. The {\em weak chromatic number} $\chi(S)$ of a block design $S$ is the smallest integer $\delta$ such that $S$ has a weak $\delta$-colourin
Externí odkaz:
http://arxiv.org/abs/2404.06066
Autor:
Rahim, Fahim, Cavenagh, Nicholas J.
A frequency rectangle of type FR$(m,n;q)$ is an $m \times n$ matrix such that each symbol from a set of size $q$ appears $n/q$ times in each row and $m/q$ times in each column. Two frequency rectangles of the same type are said to be orthogonal if, u
Externí odkaz:
http://arxiv.org/abs/2212.10706
Autor:
Rahim, Fahim, Cavenagh, Nicholas J.
The $q^k$ (full) factorial design with replication $\lambda$ is the multi-set consisting of $\lambda$ occurrences of each element of each $q$-ary vector of length $k$; we denote this by $\lambda\times [q]^k$. An $m\times n$ row-column factorial desig
Externí odkaz:
http://arxiv.org/abs/2207.02397
An ${\ell}$-cycle system ${\mathcal F}$ of a graph $\Gamma$ is a set of ${\ell}$-cycles which partition the edge set of $\Gamma$. Two such cycle systems ${\mathcal F}$ and ${\mathcal F}'$ are said to be {\em orthogonal} if no two distinct cycles from
Externí odkaz:
http://arxiv.org/abs/2203.00816
Publikováno v:
Designs, Codes and Cryptography (2021) 89:525-558
A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type $(n;\lambda)$ if it contains $n/\lambda$ symbols, each of which occurs $\lambda$ times per row and $\la
Externí odkaz:
http://arxiv.org/abs/2009.03475
Publikováno v:
Electronic Journal of Combinatorics 27 (2020), P3.7
A \emph{frequency square} is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only {\em binary} frequency squares of order $n$ with $n/2$ zeroes and $n/2$ ones in each row and column. Two such freque
Externí odkaz:
http://arxiv.org/abs/1912.08972
Autor:
Rahim, Fahim, Cavenagh, Nicholas J.
Publikováno v:
In Discrete Mathematics December 2023 346(12)
In this paper we will show the existence of a face $2$-colourable biembedding of the complete graph onto an orientable surface where each face is a cycle of a fixed length $k$, for infinitely many values of $k$. In particular, under certain condition
Externí odkaz:
http://arxiv.org/abs/1906.10525
Square Heffter arrays are $n\times n$ arrays such that each row and each column contains $k$ filled cells, each row and column sum is divisible by $2nk+1$ and either $x$ or $-x$ appears in the array for each integer $1\leq x\leq nk$. Archdeacon noted
Externí odkaz:
http://arxiv.org/abs/1906.07366
Autor:
Rahim, Fahim, Cavenagh, Nicholas J.
Publikováno v:
In Linear Algebra and Its Applications 15 June 2023 667:44-70