Paul Bastide, University of Oxford

An object U is said to be universal for a class F if all elements of F are “contained” in U under some notion of containment. Such notions have proven useful in many contexts in combinatorics and computer sicence, both to simplify proofs and to obtain efficient algorithms. This talk is discuss the following question: What is the size of the smallest poset that contains every n-element poset as an induced subposet? We will show that such a universal poset exist of size 2^2n/3 improving the previous best known bound of 2ⁿ obtained from the hypercube of dimension n.

This is based on joint work with Carla Groenland and Rajko Nenadov.