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2013 | 11 | 2 | 296-307
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
2
Strony
296-307
Opis fizyczny
Daty
wydano
2013-02-01
online
2012-11-21
Twórcy
Bibliografia
  • [1] Barát J., Hajnal P., Horváth E.K., Elementary proof techniques for the maximum number of islands, European J. Combin., 2011, 32(2), 276–281 http://dx.doi.org/10.1016/j.ejc.2010.10.001
  • [2] Czédli G., The number of rectangular islands by means of distributive lattices, European J. Combin., 2009, 30(1), 208–215 http://dx.doi.org/10.1016/j.ejc.2008.02.005
  • [3] Czédli G., Hartmann M., Schmidt E.T., CD-independent subsets in distributive lattices, Publ. Math. Debrecen, 2009, 74(1–2), 127–134
  • [4] Czédli G., Schmidt E.T., CDW-independent subsets in distributive lattices, Acta Sci. Math. (Szeged), 2009, 75(1–2), 49–53
  • [5] Foldes S., Singhi N.M., On instantaneous codes, J. Comb. Inf. Syst. Sci., 2006, 31(1–4), 307–316
  • [6] Gerstenkorn T., Tepavčevic A., Lattice valued intuitionistic fuzzy sets, Cent. Eur. J. Math., 2004, 2(3), 388–398 http://dx.doi.org/10.2478/BF02475236
  • [7] Horváth E.K., Horváth G., Németh Z., Szabó Cs., The number of square islands on a rectangular sea, Acta Sci. Math. (Szeged), 2010, 76(1–2), 35–48
  • [8] Horváth E.K., Máder A., Tepavčevic A., One-dimensional Czédli-type islands, College Math. J., 2011, 42(5), 374–378 http://dx.doi.org/10.4169/college.math.j.42.5.374
  • [9] Horváth E.K., Németh Z., Pluhár G., The number of triangular islands on a triangular grid, Period. Math. Hungar., 2009, 58(1), 25–34 http://dx.doi.org/10.1007/s10998-009-9025-7
  • [10] Horváth E.K., Šešelja B., Tepavčevic A., Cut approach to islands in rectangular fuzzy relations, Fuzzy Sets and Systems, 2010, 161(24), 3114–3126 http://dx.doi.org/10.1016/j.fss.2010.04.019
  • [11] Lengvárszky Zs., The minimum cardinality of maximal systems of rectangular islands, European J. Combin., 2009, 30(1), 216–219 http://dx.doi.org/10.1016/j.ejc.2008.02.006
  • [12] Lengvárszky Zs., Notes on systems of triangular islands, Acta Sci. Math. (Szeged), 2009, 75(3–4), 369–376
  • [13] Lengvárszky Zs., The size of maximal systems of square islands, European J. Combin., 2009, 30(4), 889–892 http://dx.doi.org/10.1016/j.ejc.2008.07.023
  • [14] Lengvárszky Zs., Pach P.P., A note on systems of rectangular islands: the continuous case, Acta Sci. Math. (Szeged), 2011, 77(1–2), 27–34
  • [15] Máder A., Makay G., The maximum number of rectangular islands, Teach. Math., 2011, 13(1), 31–44
  • [16] Máder A., Vajda R., Elementary approaches to the teaching of the combinatorial problem of rectangular islands, International Journal of Computers for Mathematical Learning, 2010, 15(3), 267–281 http://dx.doi.org/10.1007/s10758-010-9171-9
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0103-x
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