Sven Hartmann
On the Number of Covering Pairs in Specified Lattices
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

05B99 None of the above but in this section

05C35 Extremal problems, See also {90C35}

Abstract: Given a Class ${\cal F}$ of posets, let $ex({\cal F}, n)$ denote the
maximum number of covering pairs achieved by an $n$-element poset
in ${\cal F}$. We determine this number of the class of $N$-free
lattices
and give crude lower and upper bounds for the classes of ditributive
and covering lattices. The structural characterization of covering
lattices leads us to a class of lattices whose elements have a boundet
number of lower and upper covers. This class statisfies a conjecture
of Bollobas and RRival, who originally, ask for $ex({\cal L}, n)$
where
${\cal L}$ denotes the class of all lattices.
Keywords: Lattice, Covering Pairs, N-free Posets