Linear, non-homogeneous, symmetric patterns and prime power generators in numerical semigroups associated to combinatorial configurations
We prove that the numerical semigroups associated to the combinatorial configurations satisfy a family of linear, non-homogeneous, symmetric patterns. We use these patterns to prove an upper bound of the conductor and we also give an upper bound of the multiplicity. Also, we compare bounds of the conductor of numerical semigroups associated to balanced configurations, and to configurations with coprime parameters. The proof of the latter involves a bound of the conductor of prime power generated numerical semigroups.
KeywordsNumerical semigroup Combinatorial configuration Partial linear space Linear pattern Prime power generator
The authors are grateful for many helpful discussions held with Ralf Fröberg and Christian Gottlieb. They also want to thank Fernando Torres for many fruitful comments, and an anonymous referee for the idea to construct combinatorial configurations from finite affine planes. The first author is financed by the Swedish government through the National Graduate School in Computer Science (CUGS). Partial support by the Spanish MEC projects ARES (CONSOLIDER INGENIO 2010 CSD2007-00004), RIPUP (TIN2009-11689) and ICWT (TIN2012-32757), is acknowledged.
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