Split Grothendieck rings of rooted trees and skew shapes via monoid representations

DOI10.2140/involve.2019.12.1379zbMath1435.05215arXiv1812.04937OpenAlexW3102146961WikidataQ126804160 ScholiaQ126804160MaRDI QIDQ2292602

Matthew Szczesny, David Beers

Publication date: 3 February 2020

Published in: Involve (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04937

zbMATH Keywords

combinatoricsGrothendieck ringsrooted treesfield of one elementskew shapes

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Grothendieck groups (category-theoretic aspects) (18F30) Combinatorial aspects of groups and algebras (05E16)

Cites Work

• Unnamed Item
• Representation theory of finite monoids
• The Jordan canonical form for a class of zero-one matrices
• Sheaves and \(K\)-theory for \(\mathbb F_1\)-schemes
• Classical finite transformation semigroups. An introduction.
• The Hopf algebra of skew shapes, torsion sheaves on \(\mathbb{A}_{/ \mathbb{F}_1}^n\), and ideals in Hall algebras of monoid representations
• \(\mathbb{F}_{1}\) for everyone
• On the Hall algebra of semigroup representations over \(\mathbb F_1\).
• The Kronecker Product of Graphs
• Belian categories

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