Abstract. The aim of the present paper is to generalize a result of Gábor Czédli. We estimate the maximum of the number of brick islands of ${\bf m_1\times m_2\times\cdots \times m_d}$, for any $d\geq3$ and for any fixed $d$-tuple $(m_1,m_2,\ldots,m_d)$ of positive integers.
AMS Subject Classification
(1991): 05A16, 06D99
Keyword(s):
lattice,
distributive lattice,
weakly independent subset,
weak basis,
brick island,
number of islands
Received February 11, 2008, and in revised form February 18, 2008. (Registered under 6056/2009.)
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