Exhaustive generation of atomic combinatorial differential operators

General Combinatorial Differential Operators

Let D = d/dX . We develop a theory of combinatorial differential operators of the form Ω(X, D) where Ω(X, T ) is a species of structures built on two sorts, X and T , of underlying elements. These operators act on species, F (X), instead of functions. We show how to compose these operators, how to compute their adjoints and their counterparts in the context of underlying symmetric functions and...

A theory of general combinatorial differential operators

Let D = d/dX. We develop a theory of combinatorial differential operators of the form Ω(X, D) where Ω(X, T ) is an arbitrary species of structures built on two sorts, X and T , of underlying elements. These operators act on species, F (X), instead of functions. We show how to compose these operators, how to compute their adjoints and their counterparts in the context of underlying symmetric fun...

Hopf-algebraic structure of combinatorial objects and differential operators

In this paper we describe a t{opf-algebraic structure on a vector space which has as basis a family of trees, and survey some applications of this structure to combinatorics ire_Section 1, and to differential operators in _etie_2. In Section 3 we indicate some possible future directions for this work. Much of the material discussed in this paper is work-in-progress. We describe many questions a...

Exhaustive generation of gominoes

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of differ...