##### Department of Mathematics,

University of California San Diego

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### Combinatorics Seminar

## Boris Bukh

#### Carnegie Mellon University

## Enumeration of interval graphs and $d$‑representable complexes

##### Abstract:

How many essentially distinct ways are there to arrange $n$ convex sets in $\mathbb{R}^d$? Here, `essentially distinct' means with different intersection pattern'. We discuss this question both in the dimension $1$, where it amounts to counting the interval graphs, and in higher dimenions. Based on the joint works with Amzi Jeffs. Plain text abstract: How many essentially distinct ways are there to arrange n convex sets in R^d? Here, `essentially distinct' means `with different intersection pattern'. We discuss this question both in the dimension 1, where it amounts to counting the interval graphs, and in higher dimenions. Based on the joint works with Amzi Jeffs.

### March 7, 2023

### 4:00 PM

APM 7321

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