Binary Relations on the Power Set of an n-Element Set
Ross La Haye
955 Coppens Road
Green Bay, WI 54303
We define six binary relations on the power set of an n-element set
and describe their basic structure and interrelationships. An
auxiliary relation is noted that will assist in determining the
cardinalities of each. We also indicate an eighth relation that may be
of interest. We conclude the first section by computing several
quantities related to walks in the graph of the sixth relation. In the
second section we turn our attention to the basic structure and
cardinalities of the auxiliary relation noted in section one and
several additional relations. We also compute seven sums associated
with these relations and indicate connections four relations have with
Wieder's conjoint and disjoint
Full version: pdf,
(Concerned with sequences
Received January 20 2009;
revised version received February 1 2009.
Published in Journal of Integer Sequences, February 14 2009.
Revised, May 18 2010. Additional revision, April 11 2012. Another revision,
August 12 2013.
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