Discrete Mathematics Day is a forum for discrete mathematics researchers from the Ontario\/Quebec area (and beyond!) to meet and collaborate. We cover combinatorics in a broad sense, including graphs, designs, finite fields, enumeration and algorithms.<\/p>\n
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INVITED SPEAKERS<\/strong><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Richard Anstee<\/strong>\u00a0(University of British Columbia) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Ada Chan<\/strong>\u00a0(York University) <\/em>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Richard Nowakowski\u00a0<\/strong>(Dalhousie University) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Claude Tardif<\/strong>\u00a0<\/strong>(Royal Military College) <\/p>\n The Discrete Mathematics Day will be held on Friday, May 11. \u00a0There is no registration fee but we ask that people register<\/a> to give us an idea of attendance.<\/p>\n Discrete Mathematics Day gratefully acknowledges the Student Committee of the Canadian Mathematical Society, the School of Mathematics and Statistics, and the National Science and Engineering Research Council for their financial support.<\/p>\n Speaker<\/strong><\/strong>: \u00a0Richard Anstee (University of British Columbia) The notion of a forbidden configuration(s) is one way to generalize some of these results. Given a matrix F we say A has F as a configuration if some submatrix of A is a row and column permutation of F. If we define K_k to denote the kx2^k matrix of all columns on k rows, then A shatters a k-set if and only if A has K_k as a configuration. One important extremal problem is to compute forb(m,F), which is the maximum, over all m-rowed simple A where A has no configuration F, of the number of columns in A.<\/p>\n The original results of\u00a0 Sauer (72), Perles and Shelah (72), Vapnik and Chervonenkis (71) yield forb(m,K_k) exactly. We outline related results which can be viewed as asking for F for which forb(m,F) is either equal to forb(m,K_k) or asymptotically equal.<\/p>\n <\/p>\n Speaker<\/strong><\/strong>: \u00a0Ada Chan (York University) Type II matrices regained popularity in 1990’s after spin models were introduced to give link invariants. In this talk, we give a survey of type II matrices, to see where else they show up and their connections to combinatorics.<\/p>\n <\/p>\n Speaker<\/strong><\/strong>: \u00a0Richard Nowakowski <\/p>\n Speaker<\/strong><\/strong>: \u00a0Claude Tardif (Royal Military College) At one end, electoral systems are a specialized mathematical topic involving May’s theorem, Arrow’s impossibility theorem and the Gibbard\u2013Satterthwaite theorem. At the other end, talking about them to the general public confronts one with the general understanding (and misunderstanding) of arIthmetical concepts such as majority and proportions, with how people understand other electoral systems and their properties, and even how people understand other people’s understanding of electoral systems. I find it to be a fascinating subject as a mathematician, even though I am not tempted to pursue mathematical research in it.<\/p>\n <\/p>\n For accommodations click here:<\/p>\n The Business Inn Hotel<\/a> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Ashbury House B&B<\/a><\/p>\n","protected":false},"template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_links_to":"","_links_to_target":""},"daevent-type":[],"event-audience":[],"event-featured":[],"yoast_head":"\n
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Forbidden Configurations\u00a0<\/em><\/p>\n
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Type II Matrices<\/em><\/p>\n
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Herding Cats and Dogs Through a Maze-
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 An Introduction to Combinatorial Game Theory<\/em><\/em><\/p>\n
\n<\/em><\/strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Speaking about Electoral Systems to Non-mathematicians<\/em>
\n<\/em><\/p>\nLectures<\/strong><\/h3>\n
\nTitle<\/strong>: \u00a0Forbidden Configurations
\nTime<\/strong>: \u00a09:30 – 10:30
\nAbstract<\/strong>: \u00a0The notion of VC-dimension and shattered sets has had applications in Machine Learning and Covering Arrays. The problems often involve what I call simple matrices, namely (0,1)-matrices with no repeated columns. Given a set of rows S with |S|=k, we say that a matrix A shatters the k-set S if the submatrix of A formed by the rows S contains all possible k-rowed (0,1)-columns.<\/p>\n
\nTitle<\/strong>: \u00a0Type II Matrices
\nTime<\/strong>: \u00a011:00 – 12:00
\nAbstract<\/strong>: \u00a0First introduced by Sylvester in 1867 as inverse orthogonal matrices, a type II matrix is an invertible n X n matrix that has no zero entry, whose inverse can be easily obtained by inverting every entry, taking the transpose and multiplying by n^{-1}.<\/p>\n
\nTitle<\/strong>: \u00a0Herding Cats and Dogs Through a Maze—An Introduction to Combinatorial Game Theory
\nTime<\/strong>: \u00a02:30 – 3:30
\nAbstract<\/strong>: \u00a0In these games, such as Chess, Go, Checkers, the last player to move determines the winner. There is a rich theory that goes along with these games. Using the games of Cats & Dogs and Maze, I’ll introduce the basic and not-so-basic concepts. The material is easy, even though `games are hard’, and is accessible to undergraduates, although it may be disturbing to some set theorists $\\infty -1 < \\infty$.\u00a0 Unsolved games and problems will be presented along the way.<\/p>\n
\nTitle<\/strong>: \u00a0“Speaking about Electoral Systems to Non-mathematicians”
\nTime<\/strong>: \u00a04:00 – 5:00
\nAbstract<\/strong>:\u00a0I chose the subject of this talk over very specialised possibilities involving adjoint functors and Hedetniemi’s conjecture. In 2006 I followed the proceedings of the Ontario Citizens’ Assembly on electoral reform. I participated in the subsequent referendum campaign, and joined Fair Vote Canada. I have been interested in electoral systems ever since.<\/p>\n