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Cardinality of height function’s range in case of maximally many rectangular islands – computed by cuts. (English) Zbl 1258.05124

Summary: We deal with rectangular \(m\times n\) 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.

MSC:

05D99 Extremal combinatorics
05C05 Trees
05A05 Permutations, words, matrices
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