Enumeration of Numerical Semigroups {0}∪[a,b]∪[c,∞) with Same Embedding Dimension
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Abstract
We consider the set defined as
where
be the set of all integer
such that
and
be the set integer
such that
when
and
are positive integers satisfying
. It is known that
is a numerical semigroup if and only if
. This research aims to characterize the minimal system of generators for numerical semigroups
and determine the count of numerical semigroups
that share the same embedding dimension.
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References
Chommi, N. (2020). Irreducible numerical semigroups {0}∪[a,b]∪[c,∞). (Undergraduate’s thesis). Naresuan University.
Curtis, F. (1990). On formulas for the Frobenius number of a numerical semigroup. Mathematica Scandinavica, 67, 190-193. https://www.jstor.org/stable/24492663
Davison, J.L. (1994). On the linear Diophantine problem of Frobenius. Journal of Number Theory, 48, 353–363. https://doi.org/10.1006/jnth.1994.1071
Johnson, S. M. (1960). A linear diophantine problem. Canadian Journal of Mathematics, 12, 390-398. https://doi.org/10.4153/CJM-1960-033-6
Kosasirisin, P. (2020). The number of k-symmetric numerical semigroup {0}∪[a,b]∪[c,∞). (Undergraduate’s thesis). Naresuan University.
Phosri, N. (2020). The number of k-symmetric numerical semigroup {0}∪[a,b]∪[c,∞) for k=3,4,5. (Undergraduate’s thesis). Naresuan University.
Rosales, J.C. & Garcia-Sanchez, P.A. (2009). Numerical semigroups. Springer: New York.
Sylvester, J.J. (1884). Mathematical questions with their solutions. Educational Times, 41, 171-178.
Tripathi, A. (2017). Formulae for the Frobenius number in three variables. Journal of Number Theory, 170, 368-389. https://doi.org/10.1016/j.jnt.2016.05.027