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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
December 2025
|
| In: |
SIAM journal on discrete mathematics
Year: 2025, Jahrgang: 39, Heft: 4, Pages: 1953-1973 |
| ISSN: | 1095-7146 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/24M1703288
|
| Verfasserangaben: | Patrick Arras and Felix Joos |
MARC
| LEADER | 00000naa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1951207114 | ||
| 003 | DE-627 | ||
| 005 | 20260205113044.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 260205s2025 xx |||||o 00| ||eng c | ||
| 035 | |a (DE-627)1951207114 | ||
| 035 | |a (DE-599)KXP1951207114 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Arras, Patrick |e VerfasserIn |0 (DE-588)1294111302 |0 (DE-627)1851070958 |4 aut | |
| 245 | 1 | 0 | |a Independent sets in discrete tori of odd sidelength |c Patrick Arras and Felix Joos |
| 264 | 1 | |c December 2025 | |
| 300 | |a 21 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Online veröffentlicht: 3. Oktober 2025 | ||
| 500 | |a Gesehen am 05.02.2026 | ||
| 520 | |a 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. | ||
| 700 | 1 | |a Joos, Felix |d 1989- |e VerfasserIn |0 (DE-588)1075006171 |0 (DE-627)832846244 |0 (DE-576)442747438 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |a Society for Industrial and Applied Mathematics |t SIAM journal on discrete mathematics |d Philadelphia, Pa. : Soc., 1988 |g 39(2025), 4, Seite 1953-1973 |h Online-Ressource |w (DE-627)26688539X |w (DE-600)1468404-4 |w (DE-576)078589975 |x 1095-7146 |7 nnas |
| 773 | 1 | 8 | |g volume:39 |g year:2025 |g number:4 |g pages:1953-1973 |g extent:21 |a Independent sets in discrete tori of odd sidelength |
| 856 | 4 | 0 | |u https://epubs.siam.org/doi/10.1137/24M1703288 |x Verlag |z lizenzpflichtig |3 Volltext |7 1 |
| 951 | |a AR | ||
| 992 | |a 20260205 | ||
| 993 | |a Article | ||
| 994 | |a 2025 | ||
| 998 | |g 1075006171 |a Joos, Felix |m 1075006171:Joos, Felix |d 110000 |d 110300 |e 110000PJ1075006171 |e 110300PJ1075006171 |k 0/110000/ |k 1/110000/110300/ |p 2 |y j | ||
| 998 | |g 1294111302 |a Arras, Patrick |m 1294111302:Arras, Patrick |d 110000 |e 110000PA1294111302 |k 0/110000/ |p 1 |x j | ||
| 999 | |a KXP-PPN1951207114 |e 487703613X | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"relHost":[{"recId":"26688539X","name":{"displayForm":["Society for Industrial and Applied Mathematics"]},"origin":[{"publisher":"Soc.","dateIssuedDisp":"1988-","dateIssuedKey":"1988","publisherPlace":"Philadelphia, Pa."}],"id":{"eki":["26688539X"],"issn":["1095-7146"],"zdb":["1468404-4"]},"physDesc":[{"extent":"Online-Ressource"}],"title":[{"title":"SIAM journal on discrete mathematics","title_sort":"SIAM journal on discrete mathematics"}],"pubHistory":["1.1988 -"],"note":["Gesehen am 28.06.2021"],"part":{"issue":"4","extent":"21","pages":"1953-1973","text":"39(2025), 4, Seite 1953-1973","year":"2025","volume":"39"},"language":["eng"],"titleAlt":[{"title":"Journal on discrete mathematics"}],"disp":"Society for Industrial and Applied MathematicsSIAM journal on discrete mathematics","type":{"bibl":"periodical","media":"Online-Ressource"},"corporate":[{"role":"aut","display":"Society for Industrial and Applied Mathematics"}]}],"origin":[{"dateIssuedDisp":"December 2025","dateIssuedKey":"2025"}],"title":[{"title_sort":"Independent sets in discrete tori of odd sidelength","title":"Independent sets in discrete tori of odd sidelength"}],"type":{"media":"Online-Ressource","bibl":"article-journal"},"physDesc":[{"extent":"21 S."}],"id":{"eki":["1951207114"]},"recId":"1951207114","person":[{"family":"Arras","role":"aut","display":"Arras, Patrick","given":"Patrick"},{"display":"Joos, Felix","given":"Felix","role":"aut","family":"Joos"}],"note":["Online veröffentlicht: 3. Oktober 2025","Gesehen am 05.02.2026"],"language":["eng"],"name":{"displayForm":["Patrick Arras and Felix Joos"]}} | ||
| SRT | |a ARRASPATRIINDEPENDEN2025 | ||