Affine stratifications from finite misère quotients

P-flag spaces and incidence stratifications

For any finite poset P we introduce a homogeneous space as a quotient of the general linear group with the incidence group of P. When P is a chain this quotient is a flag variety; for the trivial poset our construction gives a variety recently introduced in [20]. Moreover we provide decompositions for any set in a projective space, induced by the action of the incidence group of a suitable poset. In the classical cases of Grassmannians and flag varieties we recover, depending on the choice of the poset, the partition into Schubert cells and the matroid strata. Our general framework produces, f…

Misère博弈与Misère商

Misère Games and Misère Quotients

这些课堂讲稿是根据2006年11月在以色列Rehospital的魏茨曼科学研究所举办的一个关于贫困的短期课程编写的。他们包括介绍公正的游戏，从一开始;基本的misère商建设;证明盖伊-史密斯-普兰贝克周期定理;和声明的一些最近的结果和开放的问题的主题。

《悲惨世界》的结构与分类

The structure and classification of misère quotients

一个\emph{bipartite monoid}是一个交换幺半群$\Q$连同一个标识子集$¶\subset \Q$。在本文中，我们研究了一类二部幺半群，称为\emph{misère quotients}，这是自然相关的公平组合游戏。本文介绍了一种基于$|¶| = 2$的Misère类元的结构理论，并给出了所有该类元直到同构的完整分类。一个结果是，如果$|¶| = 2$和$\Q$是有限的，那么$|\Q| = 2^n+2$或$2^n+4$。然后，我们开发的计算技术，枚举misère小的顺序，并应用它们来计数的数量的非同构的顺序最多18。我们还包括一个手动证明，有一个商的顺序~8。

误败商的有限基数

Finite Cardinalities of Misère Quotients

研究发现， partisan 误败商的有限基数除了3之外均可实现，与 impartial 误败商必须为偶数形成对比。

在公平组合博弈中驯服野生动物

Taming the wild in impartial combinatorial games

我们在公平组合对策论中引入了一个Misere商半群的构造，并论证了它是正常博弈的Sprague-Grundy理论对Misere博弈的自然推广.一路上，我们说明了如何使用该理论来描述两个野生采取和打破游戏的完整分析。

An Investigation of Partizan Misere Games

Combinatorial games are played under two different play conventions: normal play, where the last player to move wins, and \mis play, where the last player to move loses. Combinatorial games are also classified into impartial positions and partizan positions, where a position is impartial if both players have the same available moves and partizan otherwise. \Mis play games lack many of the useful calculational and theoretical properties of normal play games. Until Plambeck's indistinguishability quotient and \mis monoid theory were developed in 2004, research on \mis play games had stalled. Thi…