Combinatorial and geometric approaches to counting problems on linear matroids, graphic arrangements, and partial orders
Abstract

Computing the BDD representing all bases of a binary or ternary matroid in an outputsize sensitive manner; by using this BDD, the Tutte polynomial of the matroid and the weight enumeration of an (n, k) linear code over GF(2) and GF(3) can be computed in time proportional to the size of the BDD.

Computing the Tutte polynomial of a linear matroid over the reals via the arrangement construction algorithm in computational geometry.

Computing the number of acyclic orientations of a graph, i.e., the number of cells in the corresponding graphic arrangement, and further the number of its lowerdimensional faces.

Computing the number of ideals in a partially ordered set, i.e., the number of some faces of the corresponding cone in the graphic arrangement
Keywords
Span Tree Partial Order Boolean Function Binary Decision Diagram Hasse DiagramPreview
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