Staircase diagrams and the enumeration of smooth Schubert varieties

Abstract

In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert varieties are in bijection with a new combinatorial data structure called staircase diagrams.

Keywords

• combinatorics
• [math.math-co]mathematics [math]/combinatorics [math.co]