Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6

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 k-combinations.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000225 A000244 A000392 A001047 A001787 A002697 A002699 A003462 A006516 A007051 A007582 A010842 A016269 A027471 A027649 A028243 A032263 A036239 A036289 A038207 A053154 A053156 A056182 A066810 A082134 A083323 A084869 A090802 A090888 A094033 A094374 A112626 A133224 A133789 A134018 A134019 A134045 A134057 A134063 A134064 A134165 A134168 and A134169.)

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.

Return to Journal of Integer Sequences home page