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The goal of my research is to show that almost all maximal intersecting families in a design are trivial. This seminar will cover a proposed proof outline in the following way: discuss a potential bound on the size of a minimal generating set for a maximal intersecting family in a design, provide a bound for the total number of maximal intersecting families, and use a counting argument to conclude that almost all maximal intersecting families in a design are trivially constructed.

# Graduate Seminar Series

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Mon., Feb. 13, 2023 3:30 p.m.
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Location: CK 185 and Live Stream
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**Speaker**: Rachel Evans

**Title:** Maximal intersecting families in block graphs of 2-( *n*, *k*, 1) designs are typically trivial (99 kB)

**Abstract:**

*k*-sets from a base set of size*n*is*n*−1 choose*k*−1. The only way to construct such a family is trivially, meaning that every*k*-set in the clique contains a common element.The goal of my research is to show that almost all maximal intersecting families in a design are trivial. This seminar will cover a proposed proof outline in the following way: discuss a potential bound on the size of a minimal generating set for a maximal intersecting family in a design, provide a bound for the total number of maximal intersecting families, and use a counting argument to conclude that almost all maximal intersecting families in a design are trivially constructed.

**Live Stream:**

https://uregina-ca.zoom.us/j/94125367372