Motzkin combinatorics in linear degenerations of the flag variety
Giovanni Cerulli Irelli, Francesco Esposito, Mario Marietti

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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Algebraic structures and combinatorial models
