Paper Info
Title
Affine stratifications from finite misère quotients
Abstract
Given a morphism from an affine semigroup to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof rests on mesoprimary decomposition of monoid congruences and a novel list of equivalent conditions characterizing the existence of an affine stratification. The motivating consequence of the main result is a special case of a conjecture due to Guo and the author on the existence of affine stratifications for (the set of winning positions of) any lattice game. The special case proved here assumes that the lattice game has finite misère quotient, in the sense of Plambeck and Siegel.
Year
DOI
Venue
2010
10.1007/s10801-012-0355-3
Journal of Algebraic Combinatorics: An International Journal
Keywords
DocType
Volume
Affine semigroup,Lattice game,Mesoprimary decomposition,Misère quotient,Monoid
Journal
37
Issue
ISSN
Citations 
1
0925-9899
0
PageRank 
References 
Authors
0.34
3
1
Name
Order
Citations
PageRank
Ezra Miller1121.62