Independent sets in discrete tori of odd sidelength
Abstract. It is a well known result due to Korshunov and Sapozhenko that the hypercube in dimensions has independent sets. Jenssen and Keevash investigated in depth Cartesian powers of cycles of fixed even lengths far beyond counting independent sets. They wonder to which extent their results extend...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
December 2025
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| In: |
SIAM journal on discrete mathematics
Year: 2025, Volume: 39, Issue: 4, Pages: 1953-1973 |
| ISSN: | 1095-7146 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/24M1703288
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| Author Notes: | Patrick Arras and Felix Joos |
| Summary: | Abstract. It is a well known result due to Korshunov and Sapozhenko that the hypercube in dimensions has independent sets. Jenssen and Keevash investigated in depth Cartesian powers of cycles of fixed even lengths far beyond counting independent sets. They wonder to which extent their results extend to cycles of odd length, where not even the easiest case, counting independent sets in Cartesian powers of the triangle, is known. In this paper, we make progress on their question by providing a lower bound, which we believe to be tight. We also obtain a less precise lower bound for the number of independent sets in Cartesian powers of arbitrary odd cycles and show how to approach this question both with the cluster expansion method as well as more directly with isoperimetric inequalities. |
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| Item Description: | Online veröffentlicht: 3. Oktober 2025 Gesehen am 05.02.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7146 |