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{
    "pk": 65035,
    "title": "Order and inverses in the monoid of misère blocking games",
    "subtitle": null,
    "abstract": "This paper considers combinatorial games with the last move losing (misère play) instead of winning (normal play). Misère games form a pomonoid in which no non-zero elements are invertible; normal-play games, however, form a group with a much richer partial order. To compensate, misère researchers typically weaken the comparison relation by restricting to a subset of games, especially to a \"universe\" (closed under addition, conjugation, and options). For some well-studied universes (like the dicot and dead-ending universes), there exist finite comparison tests and also complete characterisations of their invertible elements; more recently, the invertible elements of every \"parental\" universe have been characterised. In this paper, we study the recently-defined universe of \"blocking games\" (containing both dicots and dead-ending games): we develop a finite comparison test, and we improve on the general invertibility characterisation by showing that, as in dead-ending, a game is invertible modulo blocking if and only if it is free of previous-win subpositions (or is equal to such a form).\n \nMathematics Subject Classifications: 91A46, 06F05, 20M14, 20K27\n \nKeywords: Combinatorial Game Theory, Ordered semigroups",
    "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": "Combinatorial Game Theory"
        },
        {
            "word": "Ordered semigroups"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2rg6707j",
    "frozenauthors": [
        {
            "first_name": "Alfie",
            "middle_name": "",
            "last_name": "Davies",
            "name_suffix": "",
            "institution": "Memorial University of Newfoundland, Canada",
            "department": ""
        },
        {
            "first_name": "Rebecca",
            "middle_name": "",
            "last_name": "Milley",
            "name_suffix": "",
            "institution": "Memorial University of Newfoundland, Canada",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T12:13:19-07:00",
    "date_accepted": "2026-04-20T12:13:19-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65035/galley/49845/download/"
        }
    ]
}