Relations between Powers of Dedekind Numbers and Exponential Sums Related to Them
Frank a Campo
denote the downset-lattice of the downset-lattice
of the finite poset Q
and let d2
) denote the cardinality of
We investigate relations between the numbers
their powers, where Am
is the antichain with m
elements and Am
the direct sum of Am
. In particular, we prove the
based on the construction of a
one-to-one mapping between sets of homomorphisms. Furthermore, we
derive equations and inequalities between the numbers
exponential sums of downset sizes and interval sizes related to
We apply these results in a comparison of the computational
times of algorithms for the calculation of the Dedekind numbers
), including a new algorithm.
Full version: pdf,
(Concerned with sequence
Received January 20 2018; revised versions received May 1 2018; May 2 2018.
Published in Journal of Integer Sequences, May 8 2018.
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