On the rank functions of $\mathcal{H}$-matroids
Copyright policy )On the rank functions of $\mathcal{H}$-matroids
The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm. In this note, we give a characterization of some $\mathcal{H}$-matroids by rank functions.
6 pages
FOS: Computer and information sciences, Combinatorial optimization, Discrete Mathematics (cs.DM), Matroid;H-Matroid;Simplicial complex;Rank function, Combinatorial aspects of simplicial complexes, Combinatorial aspects of matroids and geometric lattices, 05B35, 90C27, FOS: Mathematics, matroid, \(\mathcal{H}\)-matroid, simplicial complex, rank function, Mathematics - Combinatorics, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Combinatorial optimization, Discrete Mathematics (cs.DM), Matroid;H-Matroid;Simplicial complex;Rank function, Combinatorial aspects of simplicial complexes, Combinatorial aspects of matroids and geometric lattices, 05B35, 90C27, FOS: Mathematics, matroid, \(\mathcal{H}\)-matroid, simplicial complex, rank function, Mathematics - Combinatorics, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Computer Science - Discrete Mathematics
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