Adding or removing an element from a pseudo-symmetric numerical semigroup

J. C. Rosales

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 681-696
  • ISSN: 0392-4041

Abstract

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If S is a pseudo-symmetric numerical semigroup, g is its Frobenius number and S is a minimal generator of S , then S ∪ { g } , S ∖ { g } S and S ∪ { 1 2 ⁢ g , g } are also numerical semigroups. In this paper we study these constructions.

How to cite

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Rosales, J. C.. "Adding or removing an element from a pseudo-symmetric numerical semigroup." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 681-696. <http://eudml.org/doc/289627>.

@article{Rosales2006,
abstract = {If $S$ is a pseudo-symmetric numerical semigroup, $g$ is its Frobenius number and $S$ is a minimal generator of $S$, then $S \cup \\{g\\}$, $S \setminus \\{g\\}$S and $S \cup \\{\frac\{1\}\{2\}g, g\\}$ are also numerical semigroups. In this paper we study these constructions.},
author = {Rosales, J. C.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {681-696},
publisher = {Unione Matematica Italiana},
title = {Adding or removing an element from a pseudo-symmetric numerical semigroup},
url = {http://eudml.org/doc/289627},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Rosales, J. C.
TI - Adding or removing an element from a pseudo-symmetric numerical semigroup
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 681
EP - 696
AB - If $S$ is a pseudo-symmetric numerical semigroup, $g$ is its Frobenius number and $S$ is a minimal generator of $S$, then $S \cup \{g\}$, $S \setminus \{g\}$S and $S \cup \{\frac{1}{2}g, g\}$ are also numerical semigroups. In this paper we study these constructions.
LA - eng
UR - http://eudml.org/doc/289627
ER -

References

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  13. ROSALES, J. C., GARCÍA-SÁNCHEZ, P. A., Finitely generated commutative monoids, Nova Science Publishers, New York, 1999. 
  14. ROSALES, J. C. - BRANCO, M. B., Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups, J. Pure Appl. Algebra, 171 (2002), 303-314. Zbl1006.20043
  15. ROSALES, J. C. - BRANCO, M. B., Irreducible numerical semigroups with arbitrary multiplicity and embedding dimension, J. Algebra, 264 (2003), 305-315. Zbl1028.20039
  16. ROSALES, J. C. - BRANCO, M. B., Irreducible numerical semigroups, Pacific J. Math., 209 (2003), 131-143. Zbl1057.20042
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  18. SYLVESTER, J. J., Mathematical questions with their solutions, Educational Times, 41 (1884), 21. 

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