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{
    "pk": 64805,
    "title": "Symmetric edge polytopes and matching generating polynomials",
    "subtitle": null,
    "abstract": "Symmetric edge polytopes $\\mathcal{A}_G$ of type A are lattice polytopes arising from the root system $A_n$ and finite simple graphs $G$. There is a connection between $\\mathcal{A}_G$ and the Kuramoto synchronization model in physics. In particular, the normalized volume of $\\mathcal{A}_G$ plays a central role. In the present paper, we focus on a particular class of graphs. In fact, for any cactus graph $G$, we give a formula for the $h^*$-polynomial of $\\mathcal{A}_{\\widehat{G}}$ by using matching generating polynomials, where $\\widehat{G}$ is the suspension of $G$. This gives also a formula for the normalized volume of $\\mathcal{A}_{\\widehat{G}}$. Moreover, via methods from chemical graph theory, we show that for any cactus graph $G$, the $h^*$-polynomial of $\\mathcal{A}_{\\widehat{G}}$ is real-rooted. Finally, we extend the discussion to symmetric edge polytopes of type $B$, which are lattice polytopes arising from the root system $B_n$ and finite simple graphs.\nKeywords: Symmetric edge polytope, $h^*$-polynomial, interior polynomial, matching generating polynomial, $\\mu$-polynomial, real-rooted, $\\gamma$-positive.\nMathematics Subject Classifications: 05A15, 05C31, 13P10, 52B12, 52B20",
    "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": [],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5xf8d657",
    "frozenauthors": [
        {
            "first_name": "Hidefumi",
            "middle_name": "",
            "last_name": "Ohsugi",
            "name_suffix": "",
            "institution": "Department of Mathematical Sciences, School of Science, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan",
            "department": ""
        },
        {
            "first_name": "Akiyoshi",
            "middle_name": "",
            "last_name": "Tsuchiya",
            "name_suffix": "",
            "institution": "Graduate school of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8914, Japan",
            "department": ""
        }
    ],
    "date_submitted": "2021-11-12T15:38:46Z",
    "date_accepted": "2021-11-12T15:38:46Z",
    "date_published": "2021-12-15T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64805/galley/49615/download/"
        }
    ]
}