DOI: 10.12732/ijam.v38i2.3
THE FROBENIUS NUMBER OF A CLASS
OF NUMERICAL SEMIGROUPS WITH DIMENSION 4
Violeta Angjelkoska 1,§, Donco Dimovski 2,
Merita Bajrami 3
1 American University of Europe - Fon
Faculty of Informatics
Kiro Gligorov 5, Skopje - 1000
Republic of NORTH MACEDONIA
2 Macedonian Academy of Sciences and Arts
Boulevard Krste Misirkov 2, Skopje - 1000
Republic of NORTH MACEDONIA
3 University of Tetova
Faculty of Natural Sciences and Mathematics
Ilinden, nn., Tetovo - 1200
Republic of NORTH MACEDONIA
Abstract. In this paper we present a formula for Frobenius number of numerical semigroup G with emmbeding dimension 4 such that G = <n, x, y, z>, n < x < y < z, x \equiv 1(modn), y \equiv j(modn), z \equiv k(modn) and x+y+z = tn, for t \geq 2 and t \in N.
How
to cite this paper?
DOI: 10.12732/ijam.v38i2.3
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
References
[1] V. Angjelkoska, D. Dimovski, Additive semigroups of integers. Embedding
dimension of numerical seligroups, Contributions, Masa, 41 (2020), 49-55.
[2] V. Angjelkoska, D. Dimovski, I. Stojmenovska, Classes of numerical semigroups with embedding dimension 3: An algorithm for computing the Frobenius number, International Journal of Algebra, 15, No 4 (2021), 171-179.
[3] V. Angjelkoska, D. Dimovski, I. Stojmenovska, An approach in computing the Frobenius number of numerical semigroups with embedding dimension 3, International Journal of Algebra, 15, No 4 (2021), 181-190.
[4] V. Angjelkoska, D. Dimovski, I. Stojmenovska, On a class of numerical semigroups with embedding dimension equal to 4, Asian-European Journal of Mathematics, 15, No 10 (2022), 8 pages.
[5] M. Bajrami, D. Dimovski, V. Angjelkoska, An algorithm for a class of (n, j, k)–good matrices related to numerical semigroups with embedding dimension 4, Matematichki Bilten, 47(LXXIII), No 2 (2023), 85-95.
[6] M. Bajrami, D. Dimovski, V. Angjelkoska, An investigation of numerical semigroups of embedding dimension 4 through GAP, International Journal of Algebra, 17, No 1 (2023), 1-11.
[7] M. Bajrami, D. Dimovski, V. Angjelkoska, A class of integer 3 x 3 matrices related to numerical semigroups with embedding dimension 4, Asian-European Journal of Mathematics, 17, No 11 (2024), 9 pages.
[8] M. Delgado, A. Garcia-Sachez, J. Morais, NumericalSgps. A GAP package for numerical semigroups, (2015); http://www.gap-system.org.
[9] D. Dimovski, Aditivni polugrupi na celi broevi, Prilozi IX, MANU (1977), 21-25.
[10] M. Petrich, Inverse Semigroups, Wiley, Michigan (1984).
IJAM
o Home
o Contents