1,832 research outputs found
A Family of matroid intersection algorithms for the computation of approximated symbolic network functions
In recent years, the technique of simplification during generation has turned out to be very promising for the efficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simplified during their generation with any well-known symbolic network analysis method. The underlying algorithm for the different techniques is always a matroid intersection algorithm. It is shown that the most efficient technique is the two-graph method. An implementation of the simplification during generation technique with the two-graph method illustrates its benefits for the symbolic analysis of large analog circuits
Lattice path matroids: enumerative aspects and Tutte polynomials
Fix two lattice paths P and Q from (0,0) to (m,r) that use East and North
steps with P never going above Q. We show that the lattice paths that go from
(0,0) to (m,r) and that remain in the region bounded by P and Q can be
identified with the bases of a particular type of transversal matroid, which we
call a lattice path matroid. We consider a variety of enumerative aspects of
these matroids and we study three important matroid invariants, namely the
Tutte polynomial and, for special types of lattice path matroids, the
characteristic polynomial and the beta invariant. In particular, we show that
the Tutte polynomial is the generating function for two basic lattice path
statistics and we show that certain sequences of lattice path matroids give
rise to sequences of Tutte polynomials for which there are relatively simple
generating functions. We show that Tutte polynomials of lattice path matroids
can be computed in polynomial time. Also, we obtain a new result about lattice
paths from an analysis of the beta invariant of certain lattice path matroids.Comment: 28 pages, 11 figure
Matroids with nine elements
We describe the computation of a catalogue containing all matroids with up to
nine elements, and present some fundamental data arising from this cataogue.
Our computation confirms and extends the results obtained in the 1960s by
Blackburn, Crapo and Higgs. The matroids and associated data are stored in an
online database, and we give three short examples of the use of this database.Comment: 22 page
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