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Gröbner bases and convex polytopes
Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations TheExpand
Algebraic algorithms for sampling from conditional distributions
We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectralExpand
Combinatorial Commutative Algebra
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
This textbook for invariants theory and research monograph that introduces a new approach to the algorithmic side of invariant theory and students should find the book useful as an introduction to this classical and new area of mathematics. Expand
Oriented Matroids
The tropical Grassmannian
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 polyhedralExpand
Tropical Convexity
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 ofExpand
Algebraic Statistics for Computational Biology
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 andExpand
A polyhedral method for solving sparse polynomial systems
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 toExpand
Binomial Ideals
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 manyExpand