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

Eszter Horváth, Branimir Šešelja, Andreja Tepavčević (2013)

Open Mathematics

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.

Combinaisons complètes

G.-H. Niewenglowski (1874)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

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