A Möbius arithmetic incidence function

Emil Daniel Schwab and Gabriela Schwab
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 3, Pages 27–34
Full paper (PDF, 171 Kb)

Details

Authors and affiliations

Emil Daniel Schwab
Department of Mathematical Sciences
The University of Texas at El Paso
El Paso, Texas 79968, USA

Gabriela Schwab
Department of Mathematics
El Paso Community College
El Paso, Texas 79902, USA

Abstract

The aim of this note is to study a non-standard right cancellative and half-factorial Möbius monoid, and to compute its Möbius function.

Keywords

• Convolution
• right divisibility
• Möbius monoid
• half-factorial monoid
• Möbius function

AMS Classification

• 11A25.

References

1. Content, M., Lemay, F., & Leroux, P. (1980) Catégories de Möbius et fonctorialités: Un cadre général pour l’inversion de Möbius J. Combin. Theory Ser. A, 28, 169–190.
2. Lawvere, F. W., & Menni, M. (2010) The Hopf algebra of Möbius intervals, Theory and Appl. of Categories, 24, 221–265.
3. Leroux, P. (1975) Les catégories de Möbius, Cah. Topol. Géom. Diffé. Catég., 16, 280–282.
4. McCarthy, P. J. (1986) Introduction to Arithmetical Functions, Springer-Verlag, New York.
5. Schwab, E. D. (2015) Möbius monoids and their connection to inverse monoids, Semigroup Forum,90(3), 694–720.
6. Schwab, E. D., & Haukkanen, P. (2008) A unique factorization in commutative Möbius monoids, Int. J. Number Th., 14, 549–561.
7. Soppi, R. (2013) Arithmetic incidence functions. A study of factorability, University of Tampere, Licentiate Thesis, https://tampub.uta.fi/handle/10024/95043.