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{
    "pk": 64846,
    "title": "Tutte short exact sequences of graphs",
    "subtitle": null,
    "abstract": "We associate two modules, the $G$-parking critical module and the toppling critical module, to an undirected connected graph $G$. The $G$-parking critical module and the toppling critical module are canonical modules (with suitable twists) of quotient rings of the well-studied $G$-parking function ideal and the toppling ideal, respectively. For each critical module, we establish a Tutte-like short exact sequence relating the modules associated to $G$, an edge contraction $G/e$ and an edge deletion $G \\setminus e$ ($e$ is a non-bridge). We obtain purely combinatorial consequences of Tutte short exact sequences. For instance, we reprove a theorem of Merino that the critical polynomial of a graph is an evaluation of its Tutte polynomial, and relate the vanishing of certain combinatorial invariants (the number of acyclic orientations on connected partition graphs satisfying a unique sink property) of $G/e$ to the equality of the corresponding invariants of $G$ and $G \\setminus e$.\n \nMathematics Subject Classifications: 13D02, 05E40\n \nKeywords: Tutte polynomials, chip firing games, toppling ideals, $G$-parking function ideals, canonical modules",
    "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": "Tutte polynomials"
        },
        {
            "word": "chip firing games"
        },
        {
            "word": "toppling ideals"
        },
        {
            "word": "$G$-parking function ideals"
        },
        {
            "word": "canonical modules"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9297n4tn",
    "frozenauthors": [
        {
            "first_name": "Madhusudan",
            "middle_name": "",
            "last_name": "Manjunath",
            "name_suffix": "",
            "institution": "Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India",
            "department": ""
        }
    ],
    "date_submitted": "2022-06-25T19:23:44Z",
    "date_accepted": "2022-06-25T19:23:44Z",
    "date_published": "2022-06-30T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64846/galley/49656/download/"
        }
    ]
}