The Symmetrical Exchange Property for Poset Matroids
نویسندگان
چکیده
منابع مشابه
A base exchange property for regular matroids
In this paper, we show that for any two bases B and B of a regular matroid, there is an element e ∈ B such that there is a unique element f ∈ B for which both (B\{e}) ∪ {f} and (B\{f}) ∪ {e} are bases of M. This solves a problem posed by White in 1980.
متن کاملGreedy algorithms and poset matroids
We generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes.
متن کاملOn Exchange Axioms for Valuated Matroids and Valuated Delta-Matroids
Two further equivalent axioms are given for valuations of a matroid. Let M = (V,B) be a matroid on a finite set V with the family of bases B. For ω : B → R the following three conditions are equivalent: (V1) ∀B,B′ ∈ B, ∀u ∈ B −B′,∃v ∈ B′ −B: ω(B) + ω(B′) ≤ ω(B − u+ v) + ω(B′ + u− v); (V2) ∀B,B′ ∈ B with B 6= B′, ∃u ∈ B −B′,∃v ∈ B′ −B: ω(B) + ω(B′) ≤ ω(B − u+ v) + ω(B′ + u− v); (V3) ∀B,B′ ∈ B, ∀...
متن کاملOn exchange properties for Coxeter matroids and oriented matroids
We introduce new basis exchange axioms for matroids and oriented matroids. These new axioms are special cases of exchange properties for a more general class of combinatorial structures, Coxeter matroids. We refer to them as “properties” in the more general setting because they are not all equivalent, as they are for ordinary matroids, since the Symmetric Exchange Property is strictly stronger ...
متن کاملMatroids with the Circuit Cover Property
We verify a conjecture of P. Seymour (Europ. J. Combinatorics 2, p. 289) regarding circuits of a binary matroid. A circuit cover of a integer-weighted matroid (M; p) is a list of circuits of M such that each element e is in exactly p(e) circuits from the list. We characterize those binary matroids for which two obvious necessary conditions for a weighting (M; p) to have a circuit cover are also...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1993
ISSN: 0001-8708
DOI: 10.1006/aima.1993.1066