We study the number of ways to factor a natural number n into an ordered product of integers, each factor greater than one, denoted by H(n). This counting function from number the...
Abstract. Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order...
Factorizations of the cyclic permutation (1 2 . . . N) into two permutations with respectively n and m cycles, or, equivalently, unicellular bicolored maps with N edges and n whit...
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic me...