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{
    "pk": 64912,
    "title": "On a common-extendable, non-Sidorenko linear system",
    "subtitle": null,
    "abstract": "A system of linear equations in \\(\\mathbb{F}_p^n\\) is common if every two-colouring of \\(\\mathbb{F}_p^n\\) yields at least as many monochromatic solutions as a random two-colouring, asymptotically as \\(n \\to \\infty\\). By analogy to the graph-theoretic setting, Alon has asked whether any (non-Sidorenko) system of linear equations can be made uncommon by adding sufficiently many free variables. Fox, Pham and Zhao answered this question in the affirmative among systems which consist of a single equation. We answer Alon's question in the negative.\nWe also observe that the property of remaining common despite that addition of arbitrarily many free variables is closely related to a notion of commonness in which one replaces the arithmetic mean of the number of monochromatic solutions with the geometric mean, and furthermore resolve questions of Kamčev-Liebenau-Morrison.\n \nMathematics Subject Classifications: 05D10, 11B30\n \nKeywords: Sidorenko's conjecture, Sidorenko and common linear patterns",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Sidorenko's conjecture"
        },
        {
            "word": "Sidorenko and common linear patterns"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/72c5b093",
    "frozenauthors": [
        {
            "first_name": "Daniel",
            "middle_name": "",
            "last_name": "Altman",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Michigan, Ann Arbor, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2023-12-22T13:36:47Z",
    "date_accepted": "2023-12-22T13:36:47Z",
    "date_published": "2023-12-22T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64912/galley/49722/download/"
        }
    ]
}