Karen Meagher

Permanent URI for this collectionhttps://hdl.handle.net/10294/4261

Associate Professor
Chair of the Undergraduate Studies Committee

Office: CW 307.5
E-mail: karen.meagher@uregina.ca
Phone: 306-585-4886
Website: http://uregina.ca/~meagherk
Current classes
Math 110 (Calculus I), Math 122 (Linear Algebra I)

Research interests
Combinatorics and algebraic graph theory

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    An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane
    (SIAM Journal on Discrete Mathematics, 2014) 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
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    An Erdős-Ko-Rado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane
    (SIAM J. Discrete Math. 28, 2014) 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.
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    Intersecting generalized permutations
    (2014-01-21) Borg, Peter; Meagher, Karen
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    C.V.
    (2014-01-21) Meagher, Karen
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    An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups
    (European Journal of Combinatorics, 2016) 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.
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    MIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES
    (2016-06) 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.