2 citations · 8 across the 13 of their papers we have counts for
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Enumerating the Derangements of an -Cube via Möbius Inversion
Colin Bailey, Joseph Oliveira
In , the semilattice of faces of an -cube, we count the number of automorphisms of that fix a given subalgebra -- either pointwise or as a subalgebra. B…
Representations of Symmetric Implication Algebras as Multicubes
Colin Bailey, Joseph Oliveira
We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symme…
Hypergraphic Oriented Matroid Relational Dependency Flow Models of Chemical Reaction Networks
C. G. Bailey, D. W. Gull, J. S. Oliveira
In this paper we derive and present an application of hypergraphic oriented matroids for the purpose of enumerating the variable interdependencies that define the chemical complexe…
Cubic algebras and Implication Algebras
Colin Bailey, Joseph Oliveira
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consid…
The Möbius Function on Implication sublattices of a Boolean algebra
Colin Bailey, Joseph Oliveira
Let be a finite Boolean algebra. Let be the partial order of all implication sublattices of . We will compute the Möbius function on in two differe…
Free cubic implication algebras
Colin Bailey, Joseph Oliveira
We construct free cubic implication algebras with finitely many generators, and determine the size of these algebras.