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

• Autorzy: Eszter Horváth , Branimir Šešelja , Andreja Tepavčević
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Rectangular islands; Height function; Cut relations

Kategorie tematyczne

• 05C05: Trees
• 05D99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 296-307

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Eszter Horváth

• University of Szeged

autor

Branimir Šešelja

• Faculty of Sciences, University of Novi Sad

autor

Andreja Tepavčević

• Faculty of Sciences, University of Novi Sad

Bibliografia

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• [17] Pach P.P., Pluhár G., Pongrácz A., Szabó Cs., The possible number of islands on the sea, J. Math. Anal. Appl., 2011, 375(1), 8–13 http://dx.doi.org/10.1016/j.jmaa.2010.08.012
• [18] Pluhár G., The number of brick islands by means of distributive lattices, Acta Sci. Math. (Szeged), 2009, 75(1–2), 3–11
• [19] Šešelja B., Tepavčevic A., Completion of ordered structures by cuts of fuzzy sets: an overview, Fuzzy Sets and Systems, 2003, 136(1), 1–19 http://dx.doi.org/10.1016/S0165-0114(02)00365-2
• [20] Šešelja B., Tepavčevic A., Representing ordered structures by fuzzy sets: an overview, Fuzzy Sets and Systems, 2003, 136(1), 21–39 http://dx.doi.org/10.1016/S0165-0114(02)00366-4

Identyfikatory

DOI

10.2478/s11533-012-0103-x