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 language | English |
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| Pages | 649-660 |
| Number of pages | 12 |
| State | Published - 2010 |
| Event | 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States Duration: Aug 2 2010 → Aug 6 2010 |
Conference
| Conference | 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 |
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| Country/Territory | United States |
| City | San Francisco, CA |
| Period | 8/2/10 → 8/6/10 |
Keywords
- Cylindrical posets
- Homotopy type
- Morse matching
- Order complex
ASJC Scopus subject areas
- Algebra and Number Theory