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

100%

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.

On p-semirings

100%

Budimirović B. , Budimirović V. , Šešelja B.

Discussiones Mathematicae - General Algebra and Applications

2002

tom 22

nr 2

107-117

A class of semirings, so called p-semirings, characterized by a natural number p is introduced and basic properties are investigated. It is proved that every p-semiring is a union of skew rings. It is proved that for some p-semirings with non-commutative operations, this union contains rings which are commutative and possess an identity.