Graph colouring and Steenrod's problem for Stanley-Reisner rings

2025/01/17 by Donald Stanley, Masahiro Takeda, Stanley, Donald +1 · 3 citations
Mathematics · Social Sciences · #05C15 #13F55 #55N10 #55S10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics Education and Teaching Techniques #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2501.09991

openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a classical problem in algebraic topology asked by Steenrod which graded rings occur as the cohomology ring of a space. In this paper, we define an algebraic version of the graph colouring, span colouring, and observe the relation between span colourings and Steenrod's problem for graded Stanley-Reisner rings, in other words polynomial rings divided by an ideal generated by square-free monic monomials.

Cited by

• Realizing orders in rational sphere product algebras with three generators
• Realization of some Stanley-Reisner algebras and graph colorings
• Bijection Between Point-Hyperplane Anti-Flags of V(n, 2) and Non-Singular Points of O⁺(2n, 2)

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