Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Forbes, Anthony"'
Autor:
Forbes, Anthony, Rutherford, Carrie
A regular-graph design is a block design for which a pair $\{a,b\}$ of distinct points occurs in $\lambda+1$ or $\lambda$ blocks depending on whether $\{a,b\}$ is or is not an edge of a given $\delta$-regular graph. Our paper describes a specific con
Externí odkaz:
http://arxiv.org/abs/2409.10159
The design spectrum of a simple graph $G$ is the set of positive integers $n$ such that there exists an edgewise decomposition of the complete graph $K_n$ into $n(n - 1)/(2 |E(G)|)$ copies of $G$. We compute the design spectra for 7788 6-regular grap
Externí odkaz:
http://arxiv.org/abs/2401.02846
Autor:
Forbes, Anthony D.
We give direct constructions for 233 group divisible designs with block size five, mostly of type $g^u m^1$, $m > 0$.
Comment: 63 pages. This is intended as a supplement to 'Group divisible designs with block size five', Australas. J. Combin. 87
Comment: 63 pages. This is intended as a supplement to 'Group divisible designs with block size five', Australas. J. Combin. 87
Externí odkaz:
http://arxiv.org/abs/2211.14124
Autor:
Forbes, Anthony D.
We report some group divisible designs with block size five, including types $6^{15}$ and $10^{15}$. As a consequence we are able to extend the known spectrum for 5-GDDs of type $g^u$.
Comment: 11 pages. New result for this version: 5-GDD 3^45.
Comment: 11 pages. New result for this version: 5-GDD 3^45.
Externí odkaz:
http://arxiv.org/abs/2202.13911
A generalized pentagonal geometry PENT($k$,$r$,$w$) is a partial linear space, where every line is incident with $k$ points, every point is incident with $r$ lines, and for each point, $x$, the set of points not collinear with $x$ forms the point set
Externí odkaz:
http://arxiv.org/abs/2111.13599
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points that are not collinear
Externí odkaz:
http://arxiv.org/abs/2104.02760
New results on pentagonal geometries PENT(k,r) with block sizes k = 3 or k = 4 are given. In particular we completely determine the existence spectra for PENT(3,r) systems with the maximum number of opposite line pairs as well as those without any op
Externí odkaz:
http://arxiv.org/abs/2007.10810
Autor:
Forbes, Anthony D.
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line, or block, is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points that are not
Externí odkaz:
http://arxiv.org/abs/2006.15734
Autor:
Forbes, Anthony D., Griggs, Terry S.
The design spectrum has been determined for ten of the 15 graphs with six vertices and ten edges. In this paper we solve the design spectrum problem for the remaining five graphs with three possible exceptions.
Comment: 26 pages, including 15-pa
Comment: 26 pages, including 15-pa
Externí odkaz:
http://arxiv.org/abs/2004.08963
Autor:
Forbes, Anthony D.
We discuss group divisible designs with block size four and type $g^u b^1 (gu/2)^1$, where $u = 5$, 6 and 7. For integers $a$ and $b$, we prove the following. (i) A 4-GDD of type $(4a)^5 b^1 (10a)^1$ exists if and only if $a \ge 1$, $b \equiv a$ (mod
Externí odkaz:
http://arxiv.org/abs/1906.02170