The structure and classification of misère quotients
| dc.creator | Siegel, Aaron N. | |
| dc.date | 2007-03-02 | |
| dc.date.accessioned | 2026-07-07T07:49:54Z | |
| dc.date.available | 2026-07-07T07:49:54Z | |
| dc.description | A \emph{bipartite monoid} is a commutative monoid $\Q$ together with an identified subset $¶\subset \Q$. In this paper we study a class of bipartite monoids, known as \emph{misère quotients}, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with $|¶| = 2$, and give a complete classification of all such quotients up to isomorphism. One consequence is that if $|¶| = 2$ and $\Q$ is finite, then $|\Q| = 2^n+2$ or $2^n+4$. We then develop computational techniques for enumerating misère quotients of small order, and apply them to count the number of non-isomorphic quotients of order at most~18. We also include a manual proof that there is exactly one quotient of order~8. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703070 | |
| dc.identifier | http://arxiv.org/abs/math/0703070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124993 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 91A46 | |
| dc.title | The structure and classification of misère quotients | |
| dc.type | text |