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

Eszter Horváth; Branimir Šešelja; Andreja Tepavčević

Open Mathematics (2013)

  • Volume: 11, Issue: 2, page 296-307
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Eszter Horváth, Branimir Šešelja, and Andreja Tepavčević. "Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts." Open Mathematics 11.2 (2013): 296-307. <http://eudml.org/doc/269807>.

@article{EszterHorváth2013,
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.},
author = {Eszter Horváth, Branimir Šešelja, Andreja Tepavčević},
journal = {Open Mathematics},
keywords = {Rectangular islands; Height function; Cut relations; rectangular islands; height function; cut relations},
language = {eng},
number = {2},
pages = {296-307},
title = {Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts},
url = {http://eudml.org/doc/269807},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Eszter Horváth
AU - Branimir Šešelja
AU - Andreja Tepavčević
TI - Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 296
EP - 307
AB - 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.
LA - eng
KW - Rectangular islands; Height function; Cut relations; rectangular islands; height function; cut relations
UR - http://eudml.org/doc/269807
ER -

References

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