@article{Fukshansky2011361,
    Abstract = {Let N ≥ 2 and let 1 \< a 1 \< ⋯ \< a N be relatively prime integers. The Frobenius number of this N -tuple is defined to be the largest positive integer that has no representation as ∑ i = 1 N a i x i where x 1 , {\ldots} , x N are nonnegative integers. More generally, the s -Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques from the geometry of numbers to give upper and lower bounds on the s -Frobenius number for any nonnegative integer s .},
    Author = {Fukshansky, Lenny and Sch{\"u}rmann, Achill},
    File = {Bounds on generalized Frobenius numbers - Fukshansky, Schürmann (0) (0) - a - a - n.pdf},
    ISSN = {0195-6698},
    Journal = {European Journal of Combinatorics},
    Keywords = {Frobenius' problem},
    Number = {3},
    Pages = {361 - 368},
    Title = {Bounds on generalized Frobenius numbers},
    URL = {http://www.sciencedirect.com/science/article/pii/S019566981000154X},
    Volume = {32},
    Year = {2011},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S019566981000154X},
    bdsk-url-2 = {http://dx.doi.org/10.1016/j.ejc.2010.11.001},
    date-added = {2015-11-24 10:10:16 +0000},
    date-modified = {2015-11-24 13:59:25 +0000},
    doi = {10.1016/j.ejc.2010.11.001}
}

@article{Fukshansky2011361, Abstract = {Let N ≥ 2 and let 1 \< a 1 \< ⋯ \< a N be relatively prime integers. The Frobenius number of this N -tuple is defined to be the largest positive integer that has no representation as ∑ i = 1 N a i x i where x 1 , {\ldots} , x N are nonnegative integers. More generally, the s -Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques from the geometry of numbers to give upper and lower bounds on the s -Frobenius number for any nonnegative integer s .}, Author = {Fukshansky, Lenny and Sch{\"u}rmann, Achill}, File = {Bounds on generalized Frobenius numbers - Fukshansky, Schürmann (0) (0) - a - a - n.pdf}, ISSN = {0195-6698}, Journal = {European Journal of Combinatorics}, Keywords = {Frobenius' problem}, Number = {3}, Pages = {361 - 368}, Title = {Bounds on generalized Frobenius numbers}, URL = {http://www.sciencedirect.com/science/article/pii/S019566981000154X}, Volume = {32}, Year = {2011}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S019566981000154X}, bdsk-url-2 = {http://dx.doi.org/10.1016/j.ejc.2010.11.001}, date-added = {2015-11-24 10:10:16 +0000}, date-modified = {2015-11-24 13:59:25 +0000}, doi = {10.1016/j.ejc.2010.11.001} }