{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T01:44:17Z","timestamp":1768700657703,"version":"3.49.0"},"reference-count":65,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T00:00:00Z","timestamp":1695254400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the locations of complex zeroes of independence polynomials of bounded-degree hypergraphs. For graphs, this is a long-studied subject with applications to statistical physics, algorithms, and combinatorics. Results on zero-free regions for bounded-degree graphs include Shearer\u2019s result on the optimal zero-free disc, along with several recent results on other zero-free regions. Much less is known for hypergraphs. We make some steps towards an understanding of zero-free regions for bounded-degree hypergaphs by proving that all hypergraphs of maximum degree <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline1.png\"\/><jats:tex-math>\n$\\Delta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> have a zero-free disc almost as large as the optimal disc for graphs of maximum degree <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline2.png\"\/><jats:tex-math>\n$\\Delta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> established by Shearer (of radius <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline3.png\"\/><jats:tex-math>\n$\\sim 1\/(e \\Delta )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>). Up to logarithmic factors in <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline4.png\"\/><jats:tex-math>\n$\\Delta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> this is optimal, even for hypergraphs with all edge sizes strictly greater than <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline5.png\"\/><jats:tex-math>\n$2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We conjecture that for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline6.png\"\/><jats:tex-math>\n$k\\ge 3$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline7.png\"\/><jats:tex-math>\n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-uniform <jats:italic>linear<\/jats:italic> hypergraphs have a much larger zero-free disc of radius <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000330_inline8.png\"\/><jats:tex-math>\n$\\Omega (\\Delta ^{- \\frac{1}{k-1}} )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We establish this in the case of linear hypertrees.<\/jats:p>","DOI":"10.1017\/s0963548323000330","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T08:26:33Z","timestamp":1695284793000},"page":"65-84","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["On the zeroes of hypergraph independence polynomials"],"prefix":"10.1017","volume":"33","author":[{"given":"David","family":"Galvin","sequence":"first","affiliation":[]},{"given":"Gwen","family":"McKinley","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7937-7016","authenticated-orcid":false,"given":"Will","family":"Perkins","sequence":"additional","affiliation":[]},{"given":"Michail","family":"Sarantis","sequence":"additional","affiliation":[]},{"given":"Prasad","family":"Tetali","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,9,21]]},"reference":[{"key":"S0963548323000330_ref37","volume-title":"An Exponential Bound for the Probability of Nonexistence of a Specified Subgraph in a Random Graph","author":"Janson","year":"1988"},{"key":"S0963548323000330_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2021.07.005"},{"key":"S0963548323000330_ref38","unstructured":"[38] Jenssen, M. and Keevash, P. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}