Abstract
AbstractLet $$\mathbb {N}$$
N
be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$
(
N
2
,
+
)
. Let M be a plane monoid and $$p,q\in \mathbb {N}$$
p
,
q
∈
N
. We will say that an integer number n is M(p, q)-bounded if there is $$(a,b)\in M$$
(
a
,
b
)
∈
M
such that $$a+p\le n \le b-q$$
a
+
p
≤
n
≤
b
-
q
. We will denote by $${\mathrm A}(M(p,q))=\{n\in \mathbb {N}\mid n \text { is } M(p,q)\text {-bounded}\}.$$
A
(
M
(
p
,
q
)
)
=
{
n
∈
N
∣
n
is
M
(
p
,
q
)
-bounded
}
.
An $$\mathcal {A}(p,q)$$
A
(
p
,
q
)
-semigroup is a numerical semigroup S such that $$S= {\mathrm A}(M(p,q))\cup \{0\}$$
S
=
A
(
M
(
p
,
q
)
)
∪
{
0
}
for some plane monoid M. In this work we will study these kinds of numerical semigroups.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics