On the number of bijunctive functions that are invariant under a given permutation

The class of Boolean bijunctive functions is one of the Sheffer classes. The main property which makes investigations of bijunctive functions important is the property that the problem of testing the consistency of a system of equations over a Sheffer class of functions is of a polynomial complexity (see, for example, [1–4]). In this paper, we estimate the number of bijunctive functions containing a given permutation in their inertia groups with respect to the symmetric group. In particular, we describe properties and find the number of bijunctive functions invariant with respect to a unicyclic permutation of the variables.