REALISABLE SETS OF CATENARY DEGREES OF NUMERICAL MONOIDS

The catenary degrees of elements in numerical monoids of embedding dimension three

On the set of catenary degrees of finitely generated cancellative commutative monoids

The catenary degree of an element s of a cancellative commutative monoid S is a nonnegative integer measuring the distance between the irreducible factorizations of s. The catenary degree of the monoid S, defined as the supremum over all catenary degrees occurring in S, has been heavily studied as an invariant of nonunique factorization. In this paper, we investigate the set C(S) of catenary de...

Shifts of generators and delta sets of numerical monoids

Let S be a numerical monoid with minimal generating set 〈n1, . . . , nt〉. For m ∈ S, if m = Pt i=1 xini, then Pt i=1 xi is called a factorization length of m. We denote by L(m) = {m1, . . . , mk} (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by ∆(m) = {mi+1 − mi | 1 ≤ i < k } and the Delta set of S by ∆(S) = ∪m∈S∆(m). In t...

Degrees of M-fuzzy families of independent L-fuzzy sets

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

Delta Sets of Numerical Monoids Are Eventually Periodic

Let M be a numerical monoid (i.e., an additive submonoid of N0) with minimal generating set 〈n1, . . . , nt〉. For m ∈ M , if m = Pt i=1 xini, then Pt i=1 xi is called a factorization length of m. We denote by L(m) = {m1, . . . , mk} (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by ∆(m) = {mi+1 −mi | 1 ≤ i < k } and the Del...