no. 1
Digital semigroups
Brunotte, Horst1
1 Haus-Endt-Straße 88, 40593 Düsseldorf, Germany.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 67-79.

The well-known expansion of rational integers in an arbitrary integer base different from 0,1,-1 is exploited to study relations between numerical monoids and certain subsemigroups of the multiplicative semigroup of nonzero integers.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2016005
Classification : 11N25, 20M14, 11D07
Mots clés : Numerical monoid, digital representation, digital semigroup, Frobenius number
Brunotte, Horst 1

1 Haus-Endt-Straße 88, 40593 Düsseldorf, Germany. 
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Brunotte, Horst. Digital semigroups. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 67-79. doi : 10.1051/ita/2016005. http://archive.numdam.org/articles/10.1051/ita/2016005/

M. Bras-Amorós and K. Stokes, The semigroup of combinatorial configurations. Semigroup Forum 84 (2012) 91–96. | DOI | MR | Zbl

C. Frougny and A. C. Lai, Negative bases and automata. Discrete Math. Theoret. Comput. Sci. 13 (2011) 75–93. | MR | Zbl

V. Grünwald, Intorno all’aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll’aritmetica ordinaria (decimale). Giornale di matematiche di Battaglini 23 (1885) 203–221, 367. | JFM

D.E. Knuth, The Art of Computer Programming. In Vol. 2. Seminumerical algorithms, 3rd edition. Addison-Wesley, Reading, MA (1998). | MR | Zbl

D.W. Matula, Basic digit sets for radix representation. J. Assoc. Comput. Mach. 29 (1982) 1131–1143. | DOI | MR | Zbl

A.M. Robles-Pérez and J. C. Rosales, Frobenius pseudo-varieties in numerical semigroups. Ann. Mat. Pura Appl. 194 (2015) 275–287. | DOI | MR | Zbl

J.C. Rosales, M.B. Branco and D. Torrão, Sets of positive integers closed under product and the number of decimal digits. J. Number Theory 147 (2015) 1–13. | DOI | MR | Zbl

J.C. Rosales, P.A. García-Sánchez, J.I. García-García and M.B. Branco, Arf numerical semigroups. J. Algebra 276 (2004) 3–12. | DOI | MR | Zbl

K. Stokes and M. Bras-Amorós, Linear, non-homogeneous, symmetric patterns and prime power generators in numerical semigroups associated to combinatorial configurations. Semigroup Forum 88 (2014) 11–20. | DOI | MR | Zbl

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