The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra
meet and stimulate new research directions. One of the origins of algebraic statistics is the …

For a positive real α, we can consider the additive submonoid M of the real line that is
generated by the nonnegative powers of α. When α is transcendental, M is a unique …

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the
non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants …

AFFINE SEMIGROUPS HAVING A UNIQUE BETTI ELEMENT Page 1 Journal of Algebra and Its
Applications Vol. 12, No. 3 (2013) 1250177 (11 pages) c© World Scientific Publishing Company …

The Frobenius number for sequences of triangular and tetrahedral numbers - ScienceDirect
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We examine the Delta set of a cancellative and reduced atomic monoid S where every set of
lengths of the factorizations of each element in S is bounded. In particular, we show the …

A numerical semigroup is said to be universally free if it is free for any possible arrangement
of its minimal generating set. In this work, we establish that toric ideals associated with …

A numerical semigroup is a subset of the set N of nonnegative integers that is closed under
addition, contains 0 and whose complement in N is finite. The smallest positive integer …

For some numerical semigroup rings of small embedding dimension, namely those of
embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4 …