The Frobenius complex

Eric Clark, Richard Ehrenborg

Research output: Contribution to conferencePaperpeer-review

Abstract

Motivated by the classical Frobenius problem, we introduce the Frobenius poset on the integers ℤ, that is, for a sub-semigroup Λ of the non-negative integers (ℕ, +), we define the order by n ≤ Λ m if m - n ∈ Λ. When Λ is generated by two relatively prime integers a and b, we show that the order complex of an interval in the Frobenius poset is either contractible or homotopy equivalent to a sphere. We also show that when Λ is generated by the integers {a, a + d,a + 2d,. . ., a + (a - 1)d}, the order complex is homotopy equivalent to a wedge of spheres.

Original languageEnglish
Pages649-660
Number of pages12
StatePublished - 2010
Event22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States
Duration: Aug 2 2010Aug 6 2010

Conference

Conference22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Country/TerritoryUnited States
CitySan Francisco, CA
Period8/2/108/6/10

Keywords

  • Cylindrical posets
  • Homotopy type
  • Morse matching
  • Order complex

ASJC Scopus subject areas

  • Algebra and Number Theory

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