Enumeration of 2-Polymatroids on up to Seven Elements

  title={Enumeration of 2-Polymatroids on up to Seven Elements},
  author={Thomas J. Savitsky},
  journal={SIAM J. Discret. Math.},
A theory of single-element extensions of integer polymatroids analogous to that of matroids is developed. We present an algorithm to generate a catalog of 2-polymatroids, up to isomorphism. When we implemented this algorithm on a computer, obtaining all 2-polymatroids on at most seven elements, we discovered the surprising fact that the number of 2-polymatroids on seven elements fails to be unimodal in rank. 

Enumerating all the Irreducible Polynomials over Finite Field

This algorithm is based on an improved algorithm for enumerating all the Lyndon words of length $n$ in linear delay time and the known reduction of Lyndon words to irreducible polynomials.

Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding

Methods for solving CLRP built from group theoretic techniques for combinatorial generation are developed and described and several computational experiments with interesting instances of network coding and secret sharing demonstrating the utility of the method are provided.

A Complete Bibliography of Publications in the SIAM Journal on Discrete Mathematics

(1,−1) [dLL09]. (1, 2) [BKM08, DK06, DK10]. (1,≤ l) [Lai05]. (1,m+ 1, n+ 1) [BD01]. (1− ε) ex(n,C4) [BS10a]. (2 + )n [DZ01]. (3, 1)∗ [Xu09]. (7, 2) [CW09]. (9v, 4, 1) [FHMY01]. (d, k) [KS03a]. (k, l)



Matroids with nine elements

Duality in Polymatroids and Set Functions

  • G. Whittle
  • Mathematics
    Combinatorics, Probability and Computing
  • 1992
There is a unique involutary operation on the class of k-polymatroids that interchanges deletion and contraction, which generalise those of Kung [3].

On the asymptotic proportion of connected matroids

Single-element extensions of matroids

Extensions of matroids to se ts containing one additional ele ment are c ha rac te ri zed in te rm s or mod ular cuts of the latti ce or closed s ubse ts. An equivalent charac teri za ti o n is give

A catalogue of combinatorial geometries

We include in the microfiche section of this issue a catalogue of all the different geometric configurations which may be constructed from n points, n _ 8, by specifying their points, lines, planes,

Matroid Enumeration for Incidence Geometry

A new algorithm for the enumeration of non-isomorphic matroids is developed, using an encoding of oriented matroid axioms as a boolean satisfiability (SAT) problem, which succeeds to enumerate a complete list of the isomorph-free rank 4 matroIDS on 10 elements.

Matroids, trees, stable sets

Introduction.- Paths and Flows.- Bipartite Matching and Covering.- Nonbipartite Matching and Covering.- Matroids and Submodular Functions.- Trees, Branchings, and Connectors.- Cliques, Stable Sets

McKay ’ s Canonical Graph Labeling Algorithm

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Combinatorial optimization. Polyhedra and efficiency.

This book shows the combinatorial optimization polyhedra and efficiency as your friend in spending the time in reading a book.