The membership problem in jump systems

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33 Citations (Scopus)


A jump system is a set of lattice points satisfying a certain exchange axiom. This notion was introduced by Bouchet and Cunningham [2], as a common generalization of (among others) the sets of bases of a matroid and degree sequences of subgraphs of a graph. We prove, under additional assumptions, a min-max formula for the distance of a lattice point from a jump system. The conditions are met in the examples above, and so our formula contains, as special cases, Tutte'sf-factor-theorem and Edmonds' matroid intersection theorem.

Original languageEnglish
Pages (from-to)45-66
Number of pages22
JournalJournal of Combinatorial Theory. Series B
Issue number1
Publication statusPublished - May 1 1997

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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