# B. Sturmfels

- Publications
- Influence

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**public sources and our publisher partners.**Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The… Expand

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral… Expand

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.-… Expand

This textbook for invariant theory and research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner-based method is the main tool by which the central… Expand

Polynomials in one variable Grobner bases of zero-dimensional ideals Bernstein's theorem and fewnomials Resultants Primary decomposition Polynomial systems in economics Sums of squares Polynomial… Expand

A continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations. We introduce mixed subdivisions of Newton polytopes, and we apply them to… Expand

Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an… Expand

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of… Expand

Preface Part I. Introduction to the Four Themes: 1. Statistics L. Pachter and B. Sturmfels 2. Computation L. Pachter and B. Sturmfels 3. Algebra L. Pachter and B. Sturmfels 4. Biology L. Pachter and… Expand

The theory of Grbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Grbner bases from the point of view of geometric deformations. The… Expand