Authors: Horváth, Eszter K.
Šešelja, Branimir
Tepavčević, Andreja 
Title: Cardinality of height function's range in case of maximally many rectangular islands - computed by cuts
Journal: Central European Journal of Mathematics
Volume: 11
Issue: 2
First page: 296
Last page: 307
Issue Date: 1-Feb-2013
Rank: M22
ISSN: 1895-1074
DOI: 10.2478/s11533-012-0103-x
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.
Keywords: Cut relations | Height function | Rectangular islands
Publisher: Versita Warsaw
Project: NFSR of Hungary (OTKA), grant no. K83219 and by the project TAMOP-4.2.1/B-09/1/KONV-2010-0005
Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, grant “Ordered structures and applications”

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