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Full Description
This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere. The contents comprise the proceedings of the 2018 INdAM "International Meeting on Numerical Semigroups", held in Cortona, Italy. Talks at the meeting centered not only on traditional types of numerical semigroups, such as Arf or symmetric, and their usual properties, but also on related types of semigroups, such as affine, Puiseux, Weierstrass, and primary, and their applications in other branches of algebra, including semigroup rings, coding theory, star operations, and Hilbert functions. The papers in the book reflect the variety of the talks and derive from research areas including Semigroup Theory, Factorization Theory, Algebraic Geometry, Combinatorics, Commutative Algebra, Coding Theory, and Number Theory. The book is intended for researchers and students who want to learn about recent developments in the theory of numerical semigroups and its connections with other research fields.
Contents
Bernardini, M., Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors.- Borzì A., Patterns on the numerical duplication.- Bouyalat, B. and El Baghdadi, S., Primality in semigroup rings.- Delgado, M., Conjecture of Wilf: A survey.- Eliahou, S. and Fromentin, J., Gapsets of small multiplicity.- Eto K., Generic toric ideals and row-factorization matrices in numerical semigroups.- Fel Leonig G., Symmetric (not Complete Intersection) Semigroups Generated by Six Elements.- Gimenez P. and Srinivasan H., Syzygies of numerical semigroup rings, a survey through examples.- Gotti F., Irreducibility and factorizations in monoid rings.- Gotti F. and Gotti M., On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras.- Karakaș H.I., Arf Numerical Semigroups With Multiplicity 9 and 10.- Kien Do V. and Matsuoka N., Numerical semigroup rings of maximal embedding dimension with determinantal defining ideals.- Maugeri N. and Zito G., Embedding dimension of a good semigroup.- Moyano-Fernandez J. J., On multi-index filtrations associated to Weierstrass semigroups.- Oneto A. and Tamone G., On the Hilbert function of fourgenerated numerical semigroup rings • Șahin M., Lattice Ideals, Semigroups and Toric Codes.- Spirito D., The number of star operations on numerical semigroups and on related integral domains.- Steinburg N. and Wiegand R., Torsion in tensor products over one-dimensional domains.- Strazzanti F. and Watanabe K., Almost Symmetric Numerical Semigroups with Odd Generators.-Tozzo L., Poincaré series on good semigroup ideals.- Watanabe K., A short proof of Bresinskis Theorem on Gorenstein semigroup rings generated by 4 elements
