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On distributive trices

100%

Horiuchi K. , Tepavčević A.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 1

21-29

A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.

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

80%

Horváth E. , Šešelja B. , Tepavčević A.

Open Mathematics

2013

tom 11

nr 2

296-307

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.