Maximal Representations of Elements in Numerical Semigroups

Details Maximal Representations of Elements in Numerical Semigroups Maximal Representations of Elements in Numerical Semigroups

2011-02-27

arxiv.org/abs/1102.5518v1

Mathematics

Commutative Algebra

Scientific paper

Given a numerical semigroup $S = $ and $s\in S$, we consider the representations $s = c_1 a_1 + c_2 a_2 +...+ c_t a_t$ where $c_i\ge0$. Such a representation is {\em maximal} if $c_1+c_2+...+c_t$ is a maximum over all such representations of $s$. We show that the number of maximal representations, varying over the elements in $S$, is always bounded. Thus, we define $\mp(S)$ to be the maximum number of maximal representations of elements in $S$. We study maximal representations in depth when $S$ has embedding dimension 3, and establish a formula for $\mp(S)$ in this case.

Affiliated with

Also associated with

No associations

Rating

Maximal Representations of Elements in Numerical Semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Maximal Representations of Elements in Numerical Semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximal Representations of Elements in Numerical Semigroups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-54113