English

Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers

Algebraic Geometry 2022-08-03 v2 Combinatorics

Abstract

We associate a complete non-singular fan with a polygon triangulation. Such a fan appears from a certain toric Richardson variety, called of Catalan type introduced in this paper. A toric Richardson variety of Catalan type is a Fano Bott manifold. We show that toric Richardson varieties of Catalan type are classified up to isomorphism in terms of unordered binary trees. In particular, the number of isomorphism classes of nn-dimensional toric Richardson varieties of Catalan type is the (n+1)(n+1)th Wedderburn--Etherington number.

Keywords

Cite

@article{arxiv.2105.12274,
  title  = {Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers},
  author = {Eunjeong Lee and Mikiya Masuda and Seonjeong Park},
  journal= {arXiv preprint arXiv:2105.12274},
  year   = {2022}
}