Mathematics & Statistics Faculty
http://hdl.handle.net/10294/4260
2020-06-01T07:52:58ZAn Erdős-Ko-Rado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane
http://hdl.handle.net/10294/8289
An Erdős-Ko-Rado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane
Meagher, Karen; Spiga, Pablo
In this paper we prove an Erdős-Ko-Rado-type theorem for
intersecting sets of permutations. We show that an intersecting set
of maximal size in the projective general linear group \(PGL_3(q)\),
in its natural action on the points of the projective line, is
either a coset of the stabilizer of a point or a coset of the
stabilizer of a line. This gives the first evidence to the veracity
of Conjecture~\(2\) from K.~Meagher, P.~Spiga, An Erdős-Ko-Rado theorem for
the derangement graph of \(\mathrm{PGL}(2,q)\) acting on the
projective line, \( \textit{J. Comb. Theory Series A} \textbf{118} \)
(2011), 532--544.
2014-01-01T00:00:00ZAn Erdős-Ko-Rado theorem for finite \(2\)-transitive groups
http://hdl.handle.net/10294/8288
An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups
Meagher, Karen; Spiga, Pablo; Tiep, Pham Huu
We prove an analogue of the classical Erdős-Ko-Rado theorem for
intersecting sets of permutations in finite \(2\)-transitive
groups. Given a finite group \(G\) acting faithfully and
\(2\)-transitively on the set \(\Omega\), we show that an intersecting
set of maximal size in \(G\) has cardinality \(|G|/|\Omega|\). This
generalises and gives a unifying proof of some similar recent
results in the literature.
2016-01-01T00:00:00ZMIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES
http://hdl.handle.net/10294/8287
MIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES
Meagher, Karen; Ihringer, Ferdinand
In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for
some partial geometries. Specifically, we give a condition on partial geometries which implies
that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.
2016-06-01T00:00:00ZAn Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane
http://hdl.handle.net/10294/8286
An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane
Meagher, Karen; Spiga, Pablo
Let G = PGL(2, q) be the projective general linear group acting on the projec-
tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma
in S, there is a projective point p in P_q such that \pi(p)= \sigma(p). We prove that if S is
intersecting, then |S| <= q(q-1). Also, we prove that the only sets S that meet
this bound are the cosets of the stabilizer of a point of P_q.
Keywords: derangement graph, independent sets, Erdos-Ko-Rado
2014-01-01T00:00:00Z