S. G. Williamson

Depth-First Search and Kuratowski Subgraphs

Soit G=(V, E) un graphe non planaire. On montre la methode utilisant les techniques de 1ere profondeur pour extraire sur un sous-graphe de Kuratowsky en un temps O(IVI)

Symmetry operators of Kranz products

Abstract In this paper we consider the linear algebraic analogs of certain classes of combinatorial identities connected with the problem of enumeration under group actions. The relationship between symmetry operators of Kranz products with abelian characters and their underlying subgroups is explored. Some applications to combinatorics are discussed.

Central and local limit theorems applied to asymptotic enumeration. III. Matrix recursions

Abstract Let a multivariate sequence an(k) be obtained by a matrix recursion. It is shown that it is usually easy to establish central and local limit theorems for an(k). The proof requires a lemma on multisection of multivariate series which appears to be new. The applications of the limit theorems include covering by polyominoes, enumeration of plane animals, occupancy problems, 0–1 matrices, and nonexistence of critical phenomena.

Operator theoretic invariants and the enumeration theory of Pólya and de Bruijn

Abstract It has been shown by M. Marcus and others that, in regard to combinatorial matrix functions and combinatorial inequalities, it is frequently fruitful to pass immediately from the consideration of permutations to the consideration of their tensor representations. Such an approach embeds the combinatorial arguments into the framework of linear algebra and frequently results in deeper theorems. It is interesting to note that certain basic combinatorial identities concerned with pattern enumeration and combinatorial generating functions can also be put into this framework. In this paper we consider one possible way of doing this.

Ranking Algorithms for Lists of Partitions

Given an algorithm for producing a list of objects, a “ranking” algorithm or “sequential numbering scheme“ is a rule

Combinatorics for computer science

\rho

Tensor contraction and Hermitian forms

which, given an object x, computes its position

Unitary similarity of symmetry operators

m = \rho (x)

Some remarks on a class of matrix inequalities

in the list. The associated algorithm for computing

Top-down Calculus

\rho ^{ - 1}