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A survey of semisimple algebras in algebraic combinatorics
(Springer Nature, 20211021)This is a survey of semisimple algebras of current interest in algebraic combinatorics, with a focus on questions which we feel will be new and interesting to experts in group algebras, integral representation theory, and ... 
Corrigendum to “The recognition problem for table algebras and realitybased algebras” [J. Algebra 479 (2017) 173–191]
(2019)This note reports and corrects an error in the above article. 
Orders of Torsion Units of integral realitybased algebras with rational multiplicities
(2018)A realitybased algebra (RBA) is a finitedimensional associative algebra with involution over C whose distinguished basis B contains 1 and is closed under pseudoinverse. An integral RBA is one whose structure constants ... 
An ErdősKoRado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane
(SIAM J. Discrete Math. 28, 2014)In this paper we prove an ErdősKoRadotype 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 ... 
An ErdősKoRado theorem for finite \(2\)transitive groups
(European Journal of Combinatorics, 2016)We prove an analogue of the classical ErdősKoRado theorem for intersecting sets of permutations in finite \(2\)transitive groups. Given a finite group \(G\) acting faithfully and \(2\)transitively on the set ... 
MIKL´ OSMANICKAMSINGHI CONJECTURES ON PARTIAL GEOMETRIES
(201606)In this paper we give a proof of the Mikl´osManickamSinghi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, ... 
An ErdosKoRado theorem for the derangement graph of PGL(2,q) acting on the projective plane
(SIAM Journal on Discrete Mathematics, 2014)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 ... 
The enhanced principal rank characteristic sequence for skewsymmetric matrices
(Elsevier, 20150815)The enhanced principal rank characteristic sequence (eprsequence) was originally defined for an n ×n real symmetric matrix or an n ×n Hermitian matrix. Such a sequence is defined to be l1l2···ln where lk is A,S, or N ... 
On the complexity of the positive semidefinite zero forcing number
(Elsevier, 2015)The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a nontraditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ... 
Parameters Related to TreeWidth, Zero Forcing, and Maximum Nullity of a Graph
(Wiley Periodicals, Inc., 2013)Treewidth, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the ... 
On the relationship between zero forcing number and certain graph coverings
(2014)The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced ... 
The principal rank characteristic sequence over various fields
(Elsevier, 2014)Given an nbyn matrix, its principal rank characteristic sequence is a sequence of length n + 1 of 0s and 1s where, for k = 0; 1,..., n, a 1 in the kth position indicates the existence of a principal submatrix of rank ... 
The enhanced principal rank characteristic sequence
(Elsevier, 2015)The enhanced principal rank characteristic sequence (eprsequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ... 
On the null space struture associted with trees and cycles
(The Charles Babbage Research Centre, 201302)In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in ... 
Colin de Verdiere parameters of chordal graphs
(International Linear Algebra Society, 201301)The Colin de Verdi`ere parameters mu and nu are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal ... 
Minimum number of distinct eigenvalues of graphs
(International Linear Algebra Society, 201309)The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ... 
Note on NordhausGaddum problems for Colin de Verdiere type parameters
(Public Knowledge Network, 2013)We establish the bounds 4 on the Nordhaus Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The NordhausGaddum sum lower bound is conjectured ... 
The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number
(International Linear Algebra Society, 201406)Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ... 
A note on the fixedpoint iteration for the matrix equations $X\pm A^*X^{1}A=I$
(Elsevier, 2008)The fixedpoint iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations $X\pm A^*X^{1}A=I$ (the plus/minus equations). The convergence of this method ... 
Detecting and solving hyperbolic quadratic eigenvalue problems
(SIAM, 2009)Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with ...