Combinatorial methods in topology and algebra / edited by Bruno Benedetti, Emanuele Delucchi, Luca Moci.

Format:

Book

Contributor:

Benedetti, Bruno, Editor.

Delucchi, Emanuele., Editor.

Moci, Luca, Editor.

Series:

Springer INdAM Series, 2281-518X ; 12

Language:

English

Subjects (All):

Algebra.

Discrete mathematics.

Topology.

Convex geometry.

Discrete geometry.

Discrete Mathematics.

Convex and Discrete Geometry.

Local Subjects:

Algebra.

Discrete Mathematics.

Topology.

Convex and Discrete Geometry.

Physical Description:

1 online resource (222 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

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.

Contents:

1 Introduction

2 Part I

3 Extremal graph theory and face numbers of flag triangulations of manifolds

4 Combinatorial stratifications and minimality of 2-arrangements

5 Rota’s conjecture, the missing axiom, and prime cycles in toric varieties

6 Random triangular groups

7 Generalized involution models of projective reflection groups

8 Universal Gröbner bases for maximal minors of matrices of linear forms

9 Milnor fibrations of arrangements

10 Decompositions of Betti diagrams of powers of monomial ideals

11 Matroids over a ring

12 A Minimal Irreducible Triangulation of S3

13 Tropical Oriented Matroids

14 A combinatorial classification of Buchsbaum simplicial posets

15 Differences Between Nonnegative Polynomials and Sums of Squares

16 Interpolation, box splines, and lattice points in polytopes

17 Root polytopes of crystallographic root systems

18 Product formulas for volumes of flow polytopes

19 On the Topology of the Cambrian Semilattices

20 cd-index for CW-posets

21 Bipartite Rigidity

22 Balanced manifolds and pseudomanifolds

23 Some combinatorial constructions and relations with Artin groups

24 Deterministic Abelian Sandpile and square-triangle tilings

25 A special feature of quadratic monomial ideals

26 Resonant bands, local systems and Milnor fibers of real line arrangements

27 Full research papers

28 On Highly Regular Embeddings

29 Positive sum systems

30 The Sn+1 action on spherical models and supermaximal models of tipe An-1

31 h-vectors of matroid complexes.

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

ISBN:

3-319-20155-7