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{
    "pk": 64843,
    "title": "Saturation of Newton polytopes of type A and D cluster variables",
    "subtitle": null,
    "abstract": "We study Newton polytopes for cluster variables in cluster algebras $\\mathcal{A}(\\Sigma)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the cluster variables of the initial seed $\\Sigma$. The cluster variable Newton polytopes are the Newton polytopes of these Laurent polynomials. We show that if $\\Sigma$ has principal coefficients or boundary frozen variables, then all cluster variable Newton polytopes are saturated. We also characterize when these Newton polytopes are empty; that is, when they have no non-vertex lattice points.\n \nMathematics Subject Classifications: 13F60, 52B20\n \nKeywords: Cluster algebras, Newton polytopes, snake graphs",
    "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": "Cluster algebras"
        },
        {
            "word": "Newton polytopes"
        },
        {
            "word": "snake graphs"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7x0979ct",
    "frozenauthors": [
        {
            "first_name": "Amal",
            "middle_name": "",
            "last_name": "Mattoo",
            "name_suffix": "",
            "institution": "Department of Mathematics, Columbia University, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Melissa",
            "middle_name": "",
            "last_name": "Sherman-Bennett",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Michigan, Ann Arbor, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-06-25T15:57:00Z",
    "date_accepted": "2022-06-25T15:57:00Z",
    "date_published": "2022-06-30T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64843/galley/49653/download/"
        }
    ]
}