Affine stratifications from finite misère quotients

Published

Journal Article

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. © 2012 Springer Science+Business Media, LLC.

Full Text

Duke Authors

Cited Authors

  • Miller, E

Published Date

  • February 1, 2013

Published In

Volume / Issue

  • 37 / 1

Start / End Page

  • 1 - 9

Electronic International Standard Serial Number (EISSN)

  • 1572-9192

International Standard Serial Number (ISSN)

  • 0925-9899

Digital Object Identifier (DOI)

  • 10.1007/s10801-012-0355-3

Citation Source

  • Scopus