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Archive : Discrete Mathematics



Ferdinand Ihringer, University of ReginaFerdinand Ihringer, University of ReginaEWG 336Title: Ovoids in Generalizes Quadrangles Abstract: A generalized quadrangle (GQ) of order ( s, t ) consists of a set of points P and a set of lines L such that (1) each line contains exactly s + 1 points, (2) each point lies in exactly t + 1 lines, (3) a more technical condition that prevents triangles, but guarantees the existence of quadrangles. The point graph of a GQ is strongly regular. A coclique of size 1 + st of the point graph is called an ovoid . A coclique of smaller size is called a partial ovoid . In the talk we will discuss the existence of ovoids in GQs and, if they do not exist, bounds on the size of partial ovoids.4/26/2017 3:00:00 PM4/26/2017 4:00:00 PMFalse
Wei-Hsuan Yu, University of MichiganWei-Hsuan Yu, University of MichiganEWG 336New bounds for equiangular lines and spherical two-distance sets </br></br> <a href="">Abstract</a>4/4/2017 3:00:00 PM4/4/2017 4:00:00 PMFalse
Jason Williford, University of WyomingJason Williford, University of WyomingEWG 336Title: Q-polynomial association schemes with at most 5 classes Abstract: An association scheme can be thought of as a combinatorial generalization of a finite transitive permutation group, where the notion of global symmetry is replaced by certain local symmetry conditions. The definition of association scheme is due to Bose and Shimamoto in 1939, in the context of the design of experiments. Since then it has found connections to coding theory, group theory, and finite geometry. In the 1973 thesis of Philippe Delsarte, the author identified two special classes of association schemes: the so-called P-polynomial and Q-polynomial schemes. The schemes that are P-polynomial are precisely those generated by a distance-regular graph, in which Delsarte gave natural analogues to coding theory. Similarly, Delsarte gave a natural analogue to design theory in Q-polynomial schemes. However, Q-polynomial schemes have no analogous combinatorial definition. Consequently, much less is known about them then their P-polynomial counterparts. In this talk, we will discuss what is known about primitive 3-class Q-polynomial schemes, and imprimitive Q-polynomial schemes with at most 5 classes. We will also present new tables of parameter sets summarizing known constructions, non-existence results and open cases.3/17/2017 3:00:00 PM3/17/2017 4:00:00 PMFalse
John Urschel, MITJohn Urschel, MITMemorial 111Title: Trace Theorems and Drawings of Planar Graphs Abstract: The trace operator is a crucial component of the theory of boundary value problems in partial differential equations. We prove variants of the theorems on continuity and existence of right inverse of the trace operator for discrete graphs and without any underlying geometry. We use such results to motivate a new algorithm for finding pictorial representations of planar graphs.3/10/2017 3:30:00 PM3/10/2017 4:30:00 PMFalse

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