TY - CONF
T1 - The Frobenius complex
AU - Clark, Eric
AU - Ehrenborg, Richard
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - Cylindrical posets
KW - Homotopy type
KW - Morse matching
KW - Order complex
UR - https://www.scopus.com/pages/publications/84860501981
UR - https://www.scopus.com/pages/publications/84860501981#tab=citedBy
M3 - Paper
AN - SCOPUS:84860501981
SP - 649
EP - 660
T2 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Y2 - 2 August 2010 through 6 August 2010
ER -