منابع مشابه
Enumerating Matroids of Fixed Rank
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that s(n) ∼ m(n), where m(n) denotes the number of matroids on a fixed groundset of size n, and s(n) the number of sparse paving matroids. In an earlier paper, we showed that log s(n) ∼ logm(n). The bounds that we used for that result were dominated by matroids of rank r ≈ n/2. In this paper we consider the ...
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We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the higher dimensional spanning trees in a class of cell complexes. This gives a new proof of Tutte’s theorem that the number of spanning trees of a central reflex is a perfect square and solves a problem posed by...
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We present an incremental polynomial-time algorithm for enumerating all circuits of a matroid or, more generally, all minimal spanning sets for a flat. This result implies, in particular, that for a given infeasible system of linear equations, all its maximal feasible subsystems, as well as all minimal infeasible subsystems, can be enumerated in incremental polynomial time. We also show the NP-...
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A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5894