Union of Sets of Lengths of Numerical Semigroups
Let S=⟨a1,…,ap⟩ be a numerical semigroup, let s∈S and let Z(s) be its set of factorizations. The set of lengths is denoted by L(s)={L(x1,⋯,xp)∣(x1,⋯,xp)∈Z(s)}, where L(x1,⋯,xp)=x1+⋯+xp. The following sets can then be defined: W(n)={s∈S∣∃x∈Z(s)suchthatL(x)=n}, ν(n)=⋃s∈W(n)L(s)={l1<l2<⋯<lr} and Δν(n)={l2−l1,…,lr−lr−1}. In this paper, we prove that the function Δν:N→P(N) is almost periodic with period lcm(a1,ap).
2015 ◽
Vol 25
(06)
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pp. 1043-1053
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2017 ◽
Vol 16
(11)
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pp. 1750209
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2015 ◽
Vol 15
(01)
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pp. 1650007
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2018 ◽
Vol 17
(11)
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pp. 1850205
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Keyword(s):
Keyword(s):
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