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{
    "pk": 64891,
    "title": "RSK tableaux and box-ball systems",
    "subtitle": null,
    "abstract": "A box-ball system is a discrete dynamical system whose dynamics come from the balls jumping according to certain rules. A permutation on \\(n\\) objects gives a box-ball system state by assigning its one-line notation to \\(n\\) consecutive boxes. After a finite number of steps, a box-ball system will reach a steady state. From any steady state, we can construct a tableau called the soliton decomposition of the box-ball system. We prove that if the soliton decomposition of a permutation \\(w\\) is a standard tableau or if its shape coincides with the Robinson-Schensted (RS) partition of \\(w\\), then the soliton decomposition of \\(w\\) and the RS insertion tableau of \\(w\\) are equal. We also use row reading words, Knuth moves, RS recording tableaux, and a localized version of Greene's theorem (proven recently by Lewis, Lyu, Pylyavskyy, and Sen) to study various properties of a box-ball system.\n \nMathematics Subject Classifications: 05A05, 05A17, 37B15\n \nKeywords: Permutations, box-ball systems, soliton cellular automata, Young tableaux, Robinson-Schensted-Knuth correspondence, Greene's theorem, Knuth equivalence",
    "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": "Permutations"
        },
        {
            "word": "box-ball systems"
        },
        {
            "word": "soliton cellular automata"
        },
        {
            "word": "Young tableaux"
        },
        {
            "word": "Robinson-Schensted-Knuth correspondence"
        },
        {
            "word": "Greene's theorem"
        },
        {
            "word": "Knuth equivalence"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5700d4s0",
    "frozenauthors": [
        {
            "first_name": "Ben",
            "middle_name": "",
            "last_name": "Drucker",
            "name_suffix": "",
            "institution": "Pacific Northwest National Laboratory, Richland, WA, U.S.A",
            "department": ""
        },
        {
            "first_name": "Eli",
            "middle_name": "",
            "last_name": "Garcia",
            "name_suffix": "",
            "institution": "Massachusetts Institute of Technology, Cambridge, MA, U.S.A",
            "department": ""
        },
        {
            "first_name": "Emily",
            "middle_name": "",
            "last_name": "Gunawan",
            "name_suffix": "",
            "institution": "David and Judi Proctor Department of Mathematics, University of Oklahoma, Norman, OK, U.S.A",
            "department": ""
        },
        {
            "first_name": "Aubrey",
            "middle_name": "",
            "last_name": "Rumbolt",
            "name_suffix": "",
            "institution": "Charles H. McCann Technical School, North Adams, MA, U.S.A",
            "department": ""
        },
        {
            "first_name": "Rose",
            "middle_name": "",
            "last_name": "Silver",
            "name_suffix": "",
            "institution": "Khoury College of Computer Sciences, Northeastern University, Boston, MA, U.S.A",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-13T15:56:29Z",
    "date_accepted": "2023-09-13T15:56:29Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64891/galley/49701/download/"
        }
    ]
}