Geometrical Combinatorics

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects.

This book describes different probabilistic modeling methods and their applications in various areas, such as artificial intelligence, offshore platforms, social networks, and others.

This book constitutes the refereed proceedings of the 11th International Conference on Combinatorics on Words, WORDS 2017, held in Montréal, QC, Canada, in September 2017.

Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, … and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications.

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