Misere quotients for impartial games

December 4, 2006 at 11:45 pm (abstracts, algebra, math, papers, software)

Elwyn Berlekamp suggested that the title of my recent paper with Aaron Siegel, The Phi-values of various games, be changed:

I urge you to change the title. I think you have a good chance to make an impact well beyond the small circle of experts such as those who come to conferences like the one in Banff. There are many more mathematicians and algebraists out there, as well as a big computer Go community. Terms like “Phi-function” are unlikely to become buzzwords that stick, as there are many Phi functions defined by many different authors. “Misere Quotient” might well be a unique pair of words. It could quite plausibly become buzzword that would help stir up more interest in combinatorial games in general. So I think it important that your title include that pair of words.¬† I’d propose¬†a short title such as “Misere Quotients for Impartial Games”.

It’s hard to argue with that, and it’s still a preprint. So Misere Quotients for Impartial Games it is!

Permalink Leave a Comment

An invitation to combinatorial games

October 4, 2006 at 6:13 am (abstracts, lectures)

Aaron Siegel is giving talks on combinatorial games at the Institute for Advanced Study in Princeton, NJ this month, on Oct 10 and 17.

Here is his abstract in the announcement:

Combinatorial game theory is the study of combinations of two-player games with no hidden information and no chance elements. The subject has its roots in recreational mathematics, but in its modern form involves a rich interplay of ideas borrowed from algebra, combinatorics, and the theory of computation.

The first part of this talk will be a general introduction to the classical theory of partizan games. I will show how a few simple axioms give rise to the group of short games, a partially-ordered Abelian group with enormously rich structure. I will discuss how the theory can be applied to extract useful information about a diverse array of games, including Nim, Domineering, Go, and to a lesser extent Chess.

In the second half of the talk, I will briefly discuss three areas of current research in combinatorial games: the theory of misere quotients; the lattice structure of short games; and the temperature theory of Go endgames. There has been significant activity in all three topics in the last five years, but nonetheless I will be able to state some major (and reasonably elementary) open problems in each of them.

Permalink 2 Comments