Graduate Colloquium: On the Non-existence of Combinatorial Interpretations

Zsombor Kiss, USC

Title: On the Non-existence of Combinatorial Interpretations

Abstract: Given a sequence of numbers, it is often of interest to find a combinatorial interpretation. Algebraic combinatorics is particularly rich in such sequences, through its many connections with Young tableaux, for example. But what if no such interpretation exists? I will discuss what this should mean and possible approaches to proving impossibility contingent on computational complexity theoretic conjectures, and sketch two examples: the absolute value of characters of Sn (Ikenmeyer, Pak, Panova 2024) and of inverse Kostka numbers (me, as of yet unpublished).