• Who am I?
• My coordinates
• My bibliography

Who am I ?

I was born on the 22nd of September 1976. I have lived in Uccle and Ixelles. Now I am the happy owner of an apartment in Etterbeek. I went to school at Ecole des Eglantiers (primary school) and Athénée Royal de Waterloo (secundary school).  From 1994 to 1998, I studied mathematics at the Université Libre de Bruxelles.

I was (October 1998-January 2002) a PhD student in the Service de Géométrie of the Département de Mathématiques ( Université Libre de Bruxelles ). I had a grant from the Fonds National de la Recherche Scientifique. Since January 24, 2002, I am a doctor in science. From September 26, 2002 to September 26, 2003, I worked at Michigan State University with Professor Jonathan Hall, thanks to the Belgian American Education Foundation (BAEF). Then I was back in Brussels until 2008, as a Chargé de Recherche of the FNRS. I have done two short stays abroad for research: one in Michigan (July-September 2004) and one in Western Australia (March-May 2006). Since September 2008, I am a Research Associate at The University of Western Australia (Perth), working in Cheryl Praeger's team. ). I am also Collaborateur Scientifique at ULB.

My coordinates

Devillers Alice

The University of Western Australia
School of Mathematics and Statistics
35 Stirling Highway
Crawley 6009
Western Australia

Emails: adevil@ulb.ac.be, adevil@maths.uwa.edu.au
Phone: +61 8 6488 3228
Fax: +61 8 6488 1028

My bibliography

• Devillers A. and Doyen J., "Homogeneous and ultrahomogeneous linear spaces", Journal of Combinatorial Theory Ser. A 84, pp. 236-241, 1998.
• Devillers A. , "d-homogeneous and d-ultrahomogeneous linear spaces",  Journal of Combinatorial Designs, 8(5), pp. 321-329, 2000. Abstract: A linear space $S$ is $d-homogeneous$ if, whenever the linear structures induced on two subsets $S_1$ and $S_2$ of cardinality at most $d$ are isomorphic, there is at least one automorphism of $S$ mapping $S_1$ onto $S_2$. $S$ is called $d-ultrahomogeneous$ if each is-ultrahomogeneous$ if each isomorphism between the linear structures induced on two subsets of cardinality at ach isomorphism between the linear structures induced on two subsets of cardinality at most $d$ can be extended into an automorphism of $S$. We have proved (without any finiteness assumption) that every 6-homogeneous linear space is homogeneous (that is $d$-homogeneous for every positive integer $d$). Here we classify completely the finite non-trivial linear spaces that are $d$-homogeneous for $d\geq 4$ or $d$-ultrahomogeneous for $d\geq 3$. We also prove an existence theorem for infinite non-trivial 4-ultrahomogeneous linear spaces.
• Devillers A. , "Ultrahomogeneous semilinear spaces", Proceedings of the London Mathematical Society, 84, pp.35-58, 2002. Abstract:A semilinear space $S$ is $ultrahomogeneous$ if each isomorphism between the semilinear structures induced on two finite subsets can be extended to an automorphism of $S$. We give a complete classification of all finite ultrahomogeneous semilinear spaces. Our theorem extendss a result of Gardiner on graphs and a result of Devillers and Doyen on linear spaces.
• Devillers A. , "A classification of finite homogeneous semilinear spaces", Advances in Geometry 2 (4), 307-328, 2002. Abstract: A semilinear space $S$ is $homogeneous$ if, whenever the semilinear structures induced on two finite subsets $S_1$ and $S_2$ of $S$ are isomorphic, there is at least one automorphism of $S$ mapping $S_1$ onto $S_2$. We give a complete classification of all finite homogeneous semilinear spaces. Our theorem extends a result of Ronse on graphs and a result of Devillers and Doyen on linear spaces.
• Devillers A. , "Homogeneous and ultrahomogeneous Steiner systems", Journal of Combinatorial designs 11 (3), 153-161, 2003. Abstract: A Steiner system (or $t-(v,k,1)$ design) $S$ is said to be $homogeneous$ if, whenever the substructures induced on two finite subsets $S_1$ and $S_2$ of $S$ are isomorphic, there is at least one automorphism of $S$ mapping $S_1$ onto $S_2$, and is said to be $ultrahomogeneous$ if each isomorphism between the substructures induced on two finite subsets of $S$ can be extended to an automorphism of $S$. We give a complete classification of all homogeneous and ultrahomogeneous Steiner systems.
• Devillers A. , "A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type", Innovations in Incidence Geometry, 2, pp. 131-177, 2005. Abstract: A {\em partial linear space} is a non-empty set of $points$, provided with a collection of subsets called $lines$ such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is not a graph or a linear space is called proper. A partial linear space is said to be 2-ultrahomogeneous if it admits an automorphism group which is transitive on the ordered pairs of collinear points and on the ordered pairs of non-collinear points. For proper partial linear spaces, this means that the automorphism group is of rank 3. In this paper, we give a complete classification of all finite 2-ultrahomogeneous proper partial linear spaces admitting a primitive rank 3 automorphism group of almost simple type.
• Devillers A. and J.I. Hall, "Rank 3 Latin square designs", Journal of Combinatorial Theory (A), 113, pp. 894-902 (2006). Abstract: A Latin square design whose automorphism group is transitive of rank at most $3$ on points must come from the multiplication table of an elementary abelian $p$-group, for some prime $p$.
• Devillers A. and Hendrik Van Maldeghem, "Partial linear spaces built on hexagons" , European Journal of Combinatorics, 28(3), pp. 901-915 (2007). Abstract: We define four families of geometries with as point graph the graph | or its dual | of all elliptic hyperplanes of a given parabolic quadric in any finite $6$-dimensional projective space, where adjacency is given by intersecting in a tangent $4$-space. One of the classes consist of (known) semi-partial geometries. Our main result determines the complete automorphism groups of all these geometries.
• Devillers A. and Bernhard Mühlherr, "On the simple connectedness of certain subsets of buildings" , Forum Mathematicum, 19(6), pp. 955-970 (2007). Abstract: We prove a rank 3 criterion for the simple connectedness of certain subsets of buildings and we give two applications of this criterion. The first generalizes a result of Tits for Chevalley groups to 3-spherical Kac-Moody groups. The second is the proof of the simple connectedness of certain flipflop geometries introduced in a paper by Bennet-Gramlich-Hoffmann-Shpectorov.
• Devillers A., "A classification of finite partial linear spaces with a primitive rank 3 automorphism group of grid type" , European Journal of Combinatorics, 29(1), pp. 268-272 (2008). Abstract: A partial linear space is a non-empty set of $points$, provided with a collection of subsets called $lines$ such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is neither a graph nor a linear space is called proper. The aim of this paper is to classify the finite proper partial linear spaces with a primitive rank 3 automorphism group of grid type.
• Alice Devillers, Michael Giudici, Cai Heng Li and Cheryl E. Praeger, "Primitive decompositions of Johnson graphs" , Journal of Combinatorial Theory (A) 115 (6), 925-966 (2008). Abstract: A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.
• Alice Devillers, Michael Giudici, Cai Heng Li and Cheryl E. Praeger, "Some graphs related to the small Mathieu groups" , accepted. Abstract: Two different constructions are given of a rank 8 arc-transitive graph with 165 vertices and valency 8, whose automorphism group is $M_{11}$. One involves 3-subsets of an 11-set while the other involves 4-subsets of a 12-set, and the constructions are linked with the Witt designs on 11, 12 and 24 points. Four different constructions are given of a rank 9 arc-transitive graph with 55 vertices and valency 6 whose automorphism group is $\PSL(2,11)$. This graph occurs as a subgraph of the $M_{11}$ graph, and two of the constructions involve 2-subsets of an 11-set while the remaining two involve 3-subsets of an 11-set. The $\PSL(2,11)$ and $M_{11}$ graphs occur as the second and third members of a tower of graphs defined on a conjugacy class of involutions of the simple groups $A_5$, $\PSL(2,11)$, $M_{11}$ and $M_{12}$ with two involutions adjacent if they generate a special $S_3$. The first graph in the tower is the line graph of the Petersen graph while the fourth is the Johnson graph $J(12,4)$. The graphs also arise as collineation graphs of rank two truncations of various residues of certain $P$-geometries.
• Alice Devillers, Michael Giudici, "Involution graphs where the product of two adjacent vertices has order three" , to appear in J. Aust. Math. Soc. Abstract: An $S_3$-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q).
• Alice Devillers, Ralf Gramlich, Bernhard Mühlherr, "The sphericity of the complex of non-degenerate subspaces" , accepted for Journal of the London Mathematical Society. Abstract: We prove that the complex of proper non-trivial non-degenerate subspaces of a finitedimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent to a wedge of spheres. Additionally, we show that the same is true for a slightly wider class of simplicial complexes, the so-called generalized Phan geometries of type An. These generalized Phan geometries occur as relative links of the filtration studied in [14], whose sphericity implies topological finiteness properties of suitable arithmetic groups and allows for a revision of Phan’s group-theoretical local recognition [21], [22] of suitable finite groups of Lie type with simply laced diagrams.
• Alice Devillers, Bernhard Mühlherr, Hendrik Van Maldeghem, "Codistances of 3-spherical buildings" , submitted. Abstract: We show that a 3-spherical building in which each rank 2 residue is connected far away from a chamber, and each rank 3 residue is simply 2-connected far away from a chamber, admits a twinning (i.e., is one half of a twin building) as soon as it admits a codistance, i.e., a twinning with a single chamber.

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Updated: Sun February 1, 2009