Young tableaux and Arf partitions

Young tableaux and Arf partitions

The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups.We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.

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  • [1] Arf C. Une interprétation algébrique de la suite ordres de multiplicité d’une branche algébrique. Proc London Math Soc 1949; 20: 256-287 (in French).
  • [2] Barucci V, Dobbs DE, Fontana M. Maximality properties in numerical semigroups and applications to onedimensional analytically irreducible local domains. Mem Am Math Soc 1997; 125: 1-77.
  • [3] Campillo A, Farrán JI, Munuera C. On the parameters of algebraic-geometry codes related to Arf semigroups. IEEE T Inform Theory 2000; 46: 2634-2638.
  • [4] Constantin H, Houston-Edwards B, Kaplan N. Numerical sets, core partitions, and integer points in polytopes. In: Proceedings of Combinatorial and Additive Number Theory II; 2017; New York, NY, USA. pp. 99-127. [5] D’Anna M. Type sequences of numerical semigroups. Semigroup Forum 1998; 56: 1-31.
  • [6] Fulton W. Young Tableaux, With Application to Representation Theory and Geometry. New York, NY, USA: Cambridge University Press, 1997.
  • [7] García-Sánchez PA, Karakaş Hİ, Heredia BA, Rosales JC. Parametrizing Arf numerical semigroups. J Algebra Appl 2017; 16: 11.
  • [8] Høholdt T, Van Lint JH, Pellikan R. Algebraic codes. In: Pless V, Huffman WC, Brualdi RA, editors. Handbook of Coding Theory, Vol. 1. Amsterdam, the Netherlands: Elsevier, 1998. pp. 871-961.
  • [9] İlhan S, Karakaş Hİ. Arf numerical semigroups. Turk J Math 2017; 41: 1448-1457.
  • [10] Keith WJ, Nath R. Partitions with prescribed hooksets. Journal of Combinatorics and Numbers Theory 2011; 3: 39-50.
  • [11] Rosales JC, Garcia-Sánchez PA. Numerical Semigroups. New York, NY, USA: Springer, 2009.
  • [12] Rosales JC, Garcia-Sánchez PA, Garcia JI, Branco M. Arf numerical semigroups. J Algebra 2004; 276: 3-12.