Almost partitioning the hypercube into copies of a graph

Let H be an induced subgraph of the hypercube Qk, for some k. We show that for some c=c(H), the vertices of Qn can be partitioned into induced copies of H and a remainder of at most O(nc) vertices. We also show that the error term cannot be replaced by anything smaller than log

Almost partitioning the hypercube into copies of a graph

Let H be an induced subgraph of the hypercube Qk, for some k. We show that for some c=c(H), the vertices of Qn can be partitioned into induced copies of H and a remainder of at most O(nc) vertices. We also show that the error term cannot be replaced by anything smaller than log

Decomposition and enumeration in partially ordered sets

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.Includes bibliographical references (p. 123-126).by Patricia Hersh.Ph.D

Geometry of Matroids and Hyperplane Arrangements

There is a trinity relationship between hyperplane arrangements, matroids and convex polytopes. We expand and combinatorialize it as settling the complexity issue expected by Mnev's universality theorem. Based on this theory, we show that for n less than or equal to 9 every matroid tiling in the hypersimplex Delta(3,n) associated to a weighted stable hyperplane arrangement extends to a matroid subdivision of Delta(3,n) and that the bound 9 for n is sharp. As a straightforward application, we completely answer Alexeev's algebro-geometric question.Comment: 46 pages, 24 figures; v3: minor improvement