2016
DOI: 10.1007/978-3-319-41330-3
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Numerical Semigroups and Applications

Abstract: Contents 10 2. Irreducible numerical semigroups 11 2.1. Decomposition of a numerical semigroup into irreducible semigroups 15 2.2. Free numerical semigroups 15 3. Semigroup of an irreducible meromorphic curve 17 3.1. Newton-Puiseux theorem 17 3.2. The local case 27 3.3. The case of curves with one place at infinity 28 4. Minimal presentations 32 5. Factorizations 38 5.1. Length based invariants 38 5.2. Distance based invariants 41 5.3. How far is an irreducible from being prime 43 References 45

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Cited by 42 publications
(49 citation statements)
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References 11 publications
(95 reference statements)
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“…What other ways are there to order that same number of Chicken McNuggets? Well, using the relation (3, 0, 0) ∼ (0, 2, 0), we obtain at least 3 more ways, yielding (10, 0, 3), (7, 2, 3), (4,4,3), and (1,6,3).…”
Section: Relations Trades and Minimal Presentationsmentioning
confidence: 90%
See 2 more Smart Citations
“…What other ways are there to order that same number of Chicken McNuggets? Well, using the relation (3, 0, 0) ∼ (0, 2, 0), we obtain at least 3 more ways, yielding (10, 0, 3), (7, 2, 3), (4,4,3), and (1,6,3).…”
Section: Relations Trades and Minimal Presentationsmentioning
confidence: 90%
“…Chicken McNuggets were originally sold in packages of size 6, 9, or 20 pieces, and the question of how many Chicken McNuggets can be bought without breaking apart a package became a popular recreational mathematics question. More specifically, if n Chicken Mc-Nuggets can be purchased using whole packages (where n is a positive integer), then there exist nonnegative integers x 1 , x 2 , x 3 ∈ N 0 such that n = 6x 1 + 9x 2 + 20x 3 .…”
Section: Definitions and Basic Properties Of The Mc-nugget Monoidmentioning
confidence: 99%
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“…The cardinality of A(S ) is the embedding dimension of S . For an introduction to numerical semigroups please refer to [14], and also to [1], where it is explained where the names used above come from.…”
Section: Basics On Generalized Numerical Semigroupsmentioning
confidence: 99%
“…0),(1,1),(1,2)}. The sons of S 12 are:• S 18 = S 12 ∪ {(0, 1)} \ {(2, 1)} = N 2 \ {(1, 0), (2, 0), (2, 1)}, • S 19 = S 12 ∪ {(0, 1)} \ {(3, 0)} = N 2 \ {(1, 0), (2, 0), (3, 0)}, • S 20 = S 12 ∪ {(0, 1)} \ {(4, 0)} = N 2 \ {(1,0), (2, 0), (4, 0)}, • S 21 = S 12 ∪ {(0, 1)} \ {(5, 0)} = N 2 \ {(1, 0), (2, 0), (5, 0)}.…”
mentioning
confidence: 99%