A Parametrization for Nested Canalyzing Functions Abdul Salam Jarrah, Reinhard Laubenbacher and Blessilda Raposa

Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. This paper provides a parametrization for the class of nested canalyzing functions by the points of an algebraic variety over the field with two elements. This variety is defined by the set of relations that the coefficients of such a function need to satisfy. This set of relations can be considered as an algebraic model of the class of nested canalyzing functions. It is also shown that this algebraic model is interesting to study, since the set of relations generates a toric ideal. It is also shown that the class of nested canalyzing functions is the same as the class of unate cascade functions, which have been studied since the 1960s in engineering and computer science. In particular, this equivalence provides a formula for the number of nested canalyzing functions in a given number of variables.