Monday, December 12, 2022

Monday, December 12, 2022 — 11:30 to 11:30 AM EST

Title: Cameron-Liebler Sets in Permutation Groups

Speaker: Venkata Raghu Tej Pantangi Affiliation: University of Regina Location: Contact Sabrina Lato for Zoom link

Abstract: Let $G \leq S_{n}$ be a transitive permutation group. Given $i,j \in [n]$, by $x_{i\to j}$, denote the characteristic function of the set $\{g \in G\ :\ g(i)=j\}$. A Cameron-Liebler set (CL set) in $G$ is a set which is represented by a Boolean function in the linear span of $\{x_{i\to j} \ :\ (i,j)\in [n]^2\}$. These are analogous to Boolean degree 1 functions on the hypercube and to Cameron-Liebler line classes in $PG(3,q)$. Sets of the form $\{g\ : g(i)\in X\}$ and $\{g\ : \ i \in g(X)\}$ (for $i \in [n]$ and $X \subset [n]$) are canonically occurring examples of CL sets. A result of Ellis et.al, shows that all CL sets in the $S_{n}$ are canonnical. In this talk, we will demonstrate many examples with ``exotic'' CL sets. Of special interest is an exotic CL set in $PSL(2,q)$ (with $q \equiv 3 \pmod{4}$), a 2-transitive group, just like $S_{n}$. The talk is based on ongoing joint work with Jozefien D'haeseleer and Karen Meagher.

Monday, December 12, 2022 — 3:00 PM EST

Title: When all holes have the same length

Speaker: Cléophée Robin Affiliation: University of Waterloo Location: MC 6029

Abstract: A hole is an induced cycle of length at least 4. For an integer k ≥ 4, we denote by Ck, the class of graphs where every hole has length k. We have defined a new class of graphs named blowup of ℓ-templates whose all holes have length 2ℓ + 1. Using earlier results on other related classes of graphs, we did obtain the following structural theorem :

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