Frobenius Problem for Semigroups ${\sl S}(d_1,d_2,d_3)$

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dc.creatorFel, Leonid G.
dc.date2004-09-19
dc.date.accessioned2026-07-07T05:12:18Z
dc.date.available2026-07-07T05:12:18Z
dc.descriptionThe matrix representation of the set $Δ({\bf d}^3)$, ${\bf d}^3=(d_1,d_2, d_3)$, of the integers which are unrepresentable by $d_1,d_2,d_3$ is found. The diagrammatic procedure of calculation of the generating function $Φ({\bf d}^3;z)$ for the set $Δ({\bf d}^3)$ is developed. The Frobenius number $F({\bf d}^3)$, genus $G({\bf d}^3)$ and Hilbert series $H({\bf d}^3;z)$ of a graded subring for non--symmetric and symmetric semigroups ${\sf S}({\bf d}^3)$ are found. The upper bound for the number of non--zero coefficients in the polynomial numerators of Hilbert series $H({\bf d}^m;z)$ of graded subrings for non--symmetric semigroups ${\sf S} ({\bf d}^m)$ of dimension, $m\geq 4$, is established.
dc.description43 pages, 10 Figures
dc.identifierhttps://arxiv.org/abs/math/0409331
dc.identifierhttp://arxiv.org/abs/math/0409331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72527
dc.subjectNumber Theory
dc.subject11P81; 11N56; 20F55
dc.titleFrobenius Problem for Semigroups ${\sl S}(d_1,d_2,d_3)$
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