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#### The Monotone Catenary Degree of Block Monoids

(2015-07-27)

The block monoid B(G) of a finite abelian group G is the set of zero-sum sequences g1 · · · gn
such that
!n
i=1
gi = 0 with operation given by concatenation. A factorization z = α1 · · · · · αn
of length |z| = n of α ...

#### Diophantine monoids defined by a single linear equation

(2013-11-15)

This project focuses on factorization properties of submonoids of N(r); for some positive
integer r; de ned as the solution sets of certain linear equations. In particular, the goal is to
determine all irreducible elements ...

#### A prelude and fugue on a theme of factorization

(2014-04-07)

The past decade has seen much research on factorizations of elements in multiplicative
monoids and integral domains. In particular, the use of graphical representations such as
irreducible divisor graphs, compressed ...