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The Number of Khalimsky-Continuous Functions between Two Points

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Combinatorial Image Analysis (IWCIA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6636))

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Abstract

We determine the number of Khalimsky-continuous functions defined on an interval, having two fixed endpoints, and with values in ℤ, in ℕ, or in a bounded interval. The number of Khalimsky-continuous functions with two points in their codomain gives an example of the Fibonacci sequence. A recurrence formula shall be presented to determine the number of Khalimsky-continuous functions with the values in a bounded interval. Using a generating function leads us to determine the number of increasing Khalimsky-continuous functions. Considering ℕ as a codomain of these functions yields a new example of the classical Fibonacci sequence.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Stockholm University, Sweden

    Shiva Samieinia

Authors
  1. Shiva Samieinia
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Texas, 1 University Station C0803, 78712-0240, Austin, TX, USA

    Jake K. Aggarwal

  2. Department of Computer and Information Science, State University of New York at Fredonia, 280 Central Ave., 14063, Fredonia, NY, USA

    Reneta P. Barneva

  3. Mathematics Department, SUNY Buffalo State College, 1300 Elmwood Ave., 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  4. Esuela Politécnica Superior, Departamento de Ingenería Informática, Universidad Autónoma de Madrid, c/Tomas y Valiente, 11, 28049, Cantoblanco, Madrid, Spain

    Kostadin N. Koroutchev

  5. Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, c/ Senda del Rey 9, 28080, Madrid, Spain

    Elka R. Korutcheva

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© 2011 Springer-Verlag Berlin Heidelberg

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Samieinia, S. (2011). The Number of Khalimsky-Continuous Functions between Two Points. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds) Combinatorial Image Analysis. IWCIA 2011. Lecture Notes in Computer Science, vol 6636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21073-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-21073-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21072-3

  • Online ISBN: 978-3-642-21073-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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