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Cardinality of height function’s range in case of maximally many rectangular islands — computed by cuts

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Central European Journal of Mathematics

Abstract

We deal with rectangular m×n boards of square cells, using the cut technics of the height function. We investigate combinatorial properties of this function, and in particular we give lower and upper bounds for the number of essentially different cuts. This number turns out to be the cardinality of the height function’s range, in case the height function has maximally many rectangular islands.

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary

    Eszter K. Horváth

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovica 4, Novi Sad, 21000, Serbia

    Branimir Šešelja & Andreja Tepavčević

Authors
  1. Eszter K. Horváth
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  2. Branimir Šešelja
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  3. Andreja Tepavčević
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Correspondence to Eszter K. Horváth.

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Horváth, E.K., Šešelja, B. & Tepavčević, A. Cardinality of height function’s range in case of maximally many rectangular islands — computed by cuts. centr.eur.j.math. 11, 296–307 (2013). https://doi.org/10.2478/s11533-012-0103-x

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  • DOI: https://doi.org/10.2478/s11533-012-0103-x

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