##### Department of Mathematics,

University of California San Diego

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### Graduate Student Combinatorics Seminar

## Sam Spiro

#### UCSD

## The R$\ddot{\text{o}}$dl Nibble

##### Abstract:

An $(n,k,\ell)$-design is a a family of $k$-sets of $[n]$ such that every $\ell$-set is covered precisely once. The problem of determining whether or not there exists a design for a given set of parameters is a classical and difficult question in combinatorics. We ask a variant of this problem. Namely, given $k,\ell$, can one find a family of $k$-sets of $[n]$ covering every $\ell$-set \textit{at least} once that has ``approximately'' as many sets as an $(n,k,\ell)$-design would have? In this talk we will solve the above problem using the technique known as the R$\ddot{\text{o}}$ dl nibble. As time permits we will also discuss other problems in design theory, as well as other applications of the R$\ddot{\text{o}}$dl nibble technique.

### March 1, 2019

### 9:00 AM

### AP&M 5402

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