Motzkin combinatorics in linear degenerations of the flag variety

TL;DR

This paper characterizes supports for linear degenerations of flag varieties using combinatorial and homological methods, introducing excessive multisegments linked to Motzkin numbers.

Contribution

It introduces excessive multisegments as a new combinatorial tool for studying linear degenerations of flag varieties, connecting them to Motzkin numbers.

Findings

Excessive multisegments are counted by Motzkin numbers.

Provides an explicit combinatorial/homological characterization of supports.

Establishes a new link between combinatorics and algebraic geometry in flag varieties.

Abstract

We establish an explicit combinatorial/homological characterization of supports for linear degenerations of flag varieties. For such purpose, we introduce the concept of an excessive multisegment. It provides a new class of combinatorial objects counted by Motzkin numbers.