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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0103-x,
author = {Eszter Horv\'ath and Branimir \v Se\v selja and Andreja Tepav\v cevi\'c},
title = {Cardinality of height function's range in case of maximally many rectangular islands - computed by cuts},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {296-307},
zbl = {1258.05124},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0103-x}
}
Eszter Horváth; Branimir Šešelja; Andreja Tepavčević. Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts. Open Mathematics, Tome 11 (2013) pp. 296-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0103-x/
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