Combinatorial Methods in Topology and Algebra

✍ Scribed by Bruno Benedetti, Emanuele Delucchi, Luca Moci (eds.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 222
• Series: Springer INdAM Series 12
• Edition: 1
• Category: Library

✦ Synopsis

Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects.

This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory.

The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

✦ Table of Contents

Front Matter....Pages i-vii
Introduction....Pages 1-4
Front Matter....Pages 5-5
Extremal Graph Theory and Face Numbers of Flag Triangulations of Manifolds....Pages 7-10
Combinatorial Stratifications and Minimality of Two-Arrangements....Pages 11-14
Random Triangular Groups....Pages 15-18
Generalized Involution Models of Projective Reflection Groups....Pages 19-23
Universal Gröbner Bases for Maximal Minors of Matrices of Linear Forms....Pages 25-30
Torsion in the Homology of Milnor Fibers of Hyperplane Arrangements....Pages 31-36
Decompositions of Betti Diagrams of Powers of Monomial Ideals: A Stability Conjecture....Pages 37-40
Matroids Over a Ring....Pages 41-47
Tropical Oriented Matroids....Pages 49-52
Rota’s Conjecture, the Missing Axiom, and Prime Cycles in Toric Varieties....Pages 53-57
A Combinatorial Classification of Buchsbaum Simplicial Posets....Pages 59-62
Dimensional Differences Between Faces of the Cones of Nonnegative Polynomials and Sums of Squares....Pages 63-68
On a Conjecture of Holtz and Ron Concerning Interpolation, Box Splines, and Zonotopes....Pages 69-77
Root Polytopes of Crystallographic Root Systems....Pages 79-84
On Product Formulas for Volumes of Flow Polytopes....Pages 85-89
On the Topology of the Cambrian Semilattices....Pages 91-95
cd-Index for CW-Posets....Pages 97-101
Bipartite Rigidity....Pages 103-106
Front Matter....Pages 107-114
Balanced Manifolds and Pseudomanifolds....Pages 5-5
Some Combinatorial Constructions and Relations with Artin Groups....Pages 115-119
Deterministic Abelian Sandpile and Square-Triangle Tilings....Pages 121-126
A Special Feature of Quadratic Monomial Ideals....Pages 127-136
Resonant Bands, Local Systems and Milnor Fibers of Real Line Arrangements....Pages 137-142
On Highly Regular Embeddings....Pages 143-148
Front Matter....Pages 149-153
Positive Sum Systems....Pages 155-155
....Pages 157-171

✦ Subjects

Algebra; Discrete Mathematics; Topology; Convex and Discrete Geometry