2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Combinatorial Design Theory
Org: Alice Lacaze-Masmonteil (University of Regina), David Pike (Memorial University of Newfoundland) and Doug Stinson (University of Waterloo)
Org: Alice Lacaze-Masmonteil (University of Regina), David Pike (Memorial University of Newfoundland) and Doug Stinson (University of Waterloo)
- MASOOMEH AKBARI, University of Ottawa
- ANDREA BURGESS, University of New Brunswick- Saint John
- AMANDA CHAFEE, Carleton University
- SHONDA DUECK, University of Winnipeg
Cyclic partitions of complete hypergraphs and large sets of combinatorial designs [PDF]
- ANDREA BURGESS, University of New Brunswick- Saint John
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We consider cyclic partitions of the complete $k$-uniform hy\-per\-graph on a finite set $V$, and their relationship to combinatorial designs. A $t$-com\-ple\-ment\-ary $k$-hy\-per\-graph is a $k$-uniform hy\-per\-graph with vertex set $V$ and edge set $E$ for which there exists a permutation $\theta\in Sym(V)$ such that the sets $E, E^\theta, E^{\theta^2}, \ldots, E^{\theta^{t-1}}$ partition the set of all $k$-element subsets of $V$. Such a permutation $\theta$ is called a $(t,k)$-com\-ple\-ment\-ing permutation. The $t$-com\-ple\-ment\-ary $k$-hy\-per\-graphs are a natural generalization of the almost self-com\-ple\-ment\-ary graphs, since the associated $(t,k)$-complementing permutation $\theta$ decomposes the complete $k$-uniform hypergraph into $t$ isomorphic $k$-hypergraphs, which are permuted cyclically by $\theta$. When these $t$-complementary $k$-hypergraphs in the decomposition are also regular, then they form a large set of $t$ isomorphic combinatorial designs. We will look at some algebraic constructions for large sets of combinatorial designs that arise from these cyclic decompositions, including one which generalizes the well know Paley graph construction.
- ALENA ERNST, Worcester Polytechnic Institute
- CALEB JONES,, Toronto Metropolitan University
- WILLIAM KELLOUGH, Memorial University of Newfoundland
- DONALD KREHER, Michigan Technological University
- ALICE LACAZE-MASMONTEIL,, University of Regina
- SHUXING LI, University of Delaware
- TRENT MARBACH, Toronto Metropolitan University
- WILLIAM MARTIN, Worcester Polytechnic Institute
- SHAHRIYAR POURAKBAR SAFFAR, Memorial University of Newfoundland
- MATEJA SAJNA, University of Ottawa
- KIANOOSH SHOKRI, University of Ottawa
- BRETT STEVENS, Carleton University
- DOUG STINSON,, University of Waterloo
- AMY WIEBE, University of British Columbia, Okanagan
- CALEB JONES,, Toronto Metropolitan University