Routes enumeration in a Boolean with respect to intersection and nonintersection relations (Q1280321)

The author introduces the definition of a reduced algebra of binary functions, where a binary function is a function \(f:L^2\to F\) with \(L\) a finite set and \(F\) a field. Let \(\Delta\) be an equivalence relation on \(L^2\). A binary function is called a \(\Delta\)-function, if \(f(a,b) = f(c,d)\) for any \((a,b)\Delta(c,d)\). Some applications to the enumeration of routes with respect to the intersection relation and the non-intersection relation are given.