Surprising occurrences of order structures in mathematics

Gunnar Fløystad

doi:10.3934/jcd.2024027

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2025, Volume 12, Issue 1: 92-114. Doi: 10.3934/jcd.2024027

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Surprising occurrences of order structures in mathematics

Gunnar Fløystad^1,

University of Bergen, Norway

Dedicated to Hans Munthe-Kaas and Brynjulf Owren on their 60th birthdays

Received: September 2023

Revised: July 2024

Early access: August 2024

Published: January 2025

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Abstract

Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite topologies, associative algebras, subgroups of matrix groups, ideals in polynomial rings, and classes of bipartite graphs.

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Mathematics Subject Classification: Primary: 06-02; Secondary: 06A06, 13F55, 13F20, 16G10, 20G07, 54A99.

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