Triangulations

by Jesus De Loera, Joerg Rambau, Francisco Santos

2010 · Springer Science & Business Media

Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.

The Book of Havana

by Daniel Chavarria, Irina J. Davidenko, Eduardo del Llano, Ahmel Echevarría Peré, Jorge Enrique Lage, Laidi Fernández de Juan, Eduardo Heras León, Cinthia R. Paredes, Francisco López Sacha , Eduardo Angel Santiesteban

2018 · Comma Press

When a history teacher decides to throw out an old, threadbare Cuban flag, he doesn’t plan for the air of suspicion that quickly descends on him… A woman’s attempt to register ownership of her family home draws her into a bureaucratic labyrinth that requires a grasp of higher mathematics to fully comprehend… On the day of their graduation, a group of students spend the night drinking around the ‘Fountain of Youth’, ironically celebrating the bright future that doesn’t await them… The stories gathered in this anthology reflect the many complex challenges Havana’s citizens have had to endure as a result of their country’s political isolation – from the hardships of the ‘Special Period’, to the pitfalls of Cuba’s schizophrenic currency system, to the indignities of becoming a cheap tourist destination for well-heeled Westerners. Moving through various moments in its recent history, as well as through different neighbourhoods – from the prefab, Soviet-era maze of Alamar, to the bars and nightclubs of the Malecón and Vedado – these stories also demonstrate the defiance of Havana: surviving decades of economic disappointment with a flair for the comic, the surreal and the fantastical that remains as fresh as the first dreams of revolution. Translated from the Spanish by Orsola Casagrande and Séamas Carraher.

Triangulations of Oriented Matroids

by Francisco Santos

2002 · American Mathematical Soc.

We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.