Algebra and Combinatorics

Orthogonal designs of order 32 and 64 via computational algebra

Lectures in Geometric Combinatorics

The fourteen lectures in this book were prepared for the advanced undergraduate course at the Park City Mathematics Institute on Geometric Combinatorics in July 2004. They begin with the basics of polytope theory with an emphasis on geometry via the theory of Schlegel and Gale diagrams. The lectures lead up to secondary and state polytopes arising from point configurations. These polytopes are ...

Some applications of algebra to combinatorics

Stanley, R.P., Some applications of algebra to combinatorics, Discrete Applied Mathematics 34

The Many Faces of Modern Combinatorics

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 The modern face of enumerative combinatorics. . . . . . . . . . . . . . . . . . . . . . . . 3 2 Algebraic invariants and combinatorial structures . . . . . . . . . . . . . . . . . . . . . 4 3 Combinatorics and geometry. . . . . . . . . . . . . . . . . . . . . . ...

Exterior and Symmetric Algebra Methods in Algebraic Combinatorics

A full Nesterov-Todd step interior-point method for circular cone optimization

In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.