Journal
JOURNAL OF SYMBOLIC COMPUTATION
Volume 120, Issue -, Pages -Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsc.2023.102233
Keywords
Frobenius number; Pseudo-Frobenius number; Apery set; Grobner basis; Semigroup rings
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The aim of this paper is to provide an effective pseudopolynomial algorithm on a1, which computes the Apery set and the Frobenius number of S. We also find the Grobner basis of the toric ideal defined by S without using Buchberger's algorithm. As an application, special classes of semigroups generated by generalized arithmetic progressions and generalized almost arithmetic progressions are introduced and studied.
Given n ? 2 and a1, ... , an & ISIN; N. Let S = (a1, ... , an) be a semigroup. The aim of this paper is to give an effective pseudopolynomial algorithm on a1, which computes the Apery set and the Frobenius number of S. We also find the Grobner basis of the toric ideal defined by S, for the weighted degree reverse lexicographical order ≺w to x1, ..., xn, without using Buchberger's algorithm. As an application we introduce and study some special classes of semigroups. Namely, when S is generated by generalized arithmetic progressions and generalized almost arithmetic progressions with the ratio a positive or a negative number. We determine symmetric and almost symmetric semigroups generated by a generalized arithmetic progression.& COPY; 2023 Elsevier Ltd. All rights reserved.
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