Enumerating Regular Mixed-Cell Configurations

Enumerating Regular Mixed-Cell Configurations

By means of the Cayley Trick the problem of enumerating all regular ne mixed subdivisions is reduced to enumerating all regular triangulations. The set of all regular triangulations is well-understood thanks to the bijection with the vertices of the secondary polytope. However, since we are only interested in the conngurations of mixed cells in a mixed subdivision, we want to avoid dealing with...

Enumerating topological (nk)-configurations

An (nk)-configuration is a set of n points and n lines in the projective plane such that their point – line incidence graph is k-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. We provide an algorithm for generating, for given n and k, all topological (nk)-configurati...

Enumerating the Strings of a Regular Expression

Enumerating Regular Expressions and Their Languages

In this chapter we discuss the problem of enumerating distinct regular expressions bysize and the regular languages they represent. We discuss various notions of the size of a regularexpression that appear in the literature and their advantages and disadvantages. We consider aformal definition of regular expressions using a context-free grammar.We then show how to enumerate stri...

Enumerating the nonisomorphic assembly configurations of modular robotic systems

A \modular" robotic system consists of joint and link modules that can be assembled in a variety of conngurations to meet diierent or changing task requirements. However, due to typical symmetries in module design, diierent assembly conngurations may lead to robotic structures which are kinematically identical, or isomorphic. This paper considers how to enumerate the non-isomorphic assembly con...