Name
Abstract | ||
|---|---|---|
This article studies the polyhedral structure and combinatorics of polytopes that arise from hierarchical models in statistics, and shows how to construct Gröbner bases of toric ideals associated to a subset of such models. We study the polytopes for Cyclic models, and we give a complete polyhedral description of these polytopes in the binary cyclic case. Further, we show how to build Gröbner bases of a reducible model from the Gröbner bases of its pieces. This result also gives a different proof that decomposable models have quadratic Gröbner bases. Finally, we present the solution of a problem posed by Vlach (Discrete Appl. Math. 13 (1986) 61-78) concerning the dimension of fibers coming from models corresponding to the boundary of a simplex. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jcta.2002.3301 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
article study,discrete appl,complete polyhedral description,decomposable model,bner base,different proof,binary cyclic case,cyclic model,quadratic gr,polyhedral structure,polyhedral geometry,hierarchical model | Discrete mathematics,Combinatorics,Quadratic equation,Simplex,Polytope,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
100 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
15 | 4.77 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Serkan Hosten | 1 | 65 | 13.64 |
| Seth Sullivant | 2 | 93 | 19.17 |