Graph colouring and Steenrod's problem for Stanley-Reisner rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929679948054528 |
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| author | Stanley, Donald Takeda, Masahiro |
| author_facet | Stanley, Donald Takeda, Masahiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph colouring and Steenrod's problem for Stanley-Reisner rings Stanley, Donald Takeda, Masahiro Algebraic Topology Combinatorics 55N10, 55S10, 13F55, 05C15 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. |
| title | Graph colouring and Steenrod's problem for Stanley-Reisner rings |
| topic | Algebraic Topology Combinatorics 55N10, 55S10, 13F55, 05C15 |
| url | https://arxiv.org/abs/2501.09991 |