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Gröbner bases and convex polytopes

- B. Sturmfels
- Mathematics
- 14 December 1995

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

Algebraic algorithms for sampling from conditional distributions

- P. Diaconis, B. Sturmfels
- Mathematics
- 1 February 1998

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

Combinatorial Commutative Algebra

- Ezra Miller, B. Sturmfels
- Mathematics
- 2004

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

Algorithms in invariant theory

- B. Sturmfels
- Mathematics, Computer Science
- Texts and monographs in symbolic computation
- 1993

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The tropical Grassmannian

- D. Speyer, B. Sturmfels
- Mathematics
- 16 April 2003

In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a polyhedral… Expand

Tropical Convexity

- M. Develin, B. Sturmfels
- Mathematics
- 27 August 2003

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

Algebraic Statistics for Computational Biology

- L. Pachter, B. Sturmfels
- Mathematics
- 1 August 2005

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

A polyhedral method for solving sparse polynomial systems

- Birkett Huber, B. Sturmfels
- Mathematics
- 1 October 1995

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

Binomial Ideals

- D. Eisenbud, B. Sturmfels
- Mathematics
- 11 January 1994

We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many… Expand

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