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In this paper, we construct two infinite families of tight sets with parameters $(q^{2r-2}-1)$ and $(q^{2r-1}-q^{2r-2})$, respectively, in the Hermitian polar space $\mathcal{H}(2r-1,q^2)$ for any $r\ge 2$ and any prime power $q$. Both families admit
Externí odkaz:
http://arxiv.org/abs/2112.10097
Let $H$ be a non-empty set of hyperplanes in $PG(4,q)$, $q$ even, such that every point of $PG(4,q)$ lies in either $0$, $\frac12q^3$ or $\frac12(q^3+q^2)$ hyperplanes of $ H$, and every plane of $PG(4,q)$ lies in $0$ or at least $\frac12q$ hyperplan
Externí odkaz:
http://arxiv.org/abs/1906.04932
Let $E$ be a set of solids (hyperplanes) in $PG(4,q)$, $q$ even, $q>2$, such that every point of $PG(4,q)$ lies in either $0$, $\frac12q^3$ or $\frac12(q^3-q^2)$ solids of $E$, and every plane of $PG(4,q)$ lies in either $0$, $\frac12q$ or $q$ solids
Externí odkaz:
http://arxiv.org/abs/1906.03985
We derive upper and lower bounds for the vertex-isoperimetric number of the incidence graphs of unitals and determine its order of magnitude. In the case when a unital contains sufficiently large arcs, these bounds agree and give rise to the precise
Externí odkaz:
http://arxiv.org/abs/1712.02023
Autor:
Hui, Alice M. W., Rodrigues, Bernardo
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters $(2^n\pm2^{(n-1)/2},2^{n-1}\pm2^{(n-1)/2},2^{n-2}\pm2^{(n-3)/2},2^{n-2}\pm2^{
Externí odkaz:
http://arxiv.org/abs/1605.07400
Autor:
Hui, Alice M. W.
Using geometric methods and without invoking deep results from group theory, we prove that a classical unital of even order $n\geq4$ is characterized by two conditions (I) and (II): (I) is the absence of O'Nan configurations of four distinct lines in
Externí odkaz:
http://arxiv.org/abs/1603.07557
Publikováno v:
In Journal of Combinatorial Theory, Series A August 2021 182
Publikováno v:
In Discrete Mathematics June 2020 343(6)
Akademický článek
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Autor:
Hui, Alice M.W., Wong, Philip P.W.
Publikováno v:
In Journal of Combinatorial Theory, Series A February 2014 122:39-52