Matroids Whose Ground Sets are Domains of Functions
From an integer-valued function f we obtain, in a natural way, a matroid Mf on the domain of f. We show that the class of matroids so obtained is closed under restriction, contraction, duality, truncation and elongation, but not under direct sum. We give an excluded-minor characterization of and show that consists precisely of those transversal matroids with a presentation in which the sets in the presentation are nested. Finally, we show that on an n-set there are exactly 2”. © 1982, Australian Mathematical Society. All rights reserved.
Publication Source (Journal or Book title)
Journal of the Australian Mathematical Society
Oxley, J. (1982). Matroids Whose Ground Sets are Domains of Functions. Journal of the Australian Mathematical Society, 32 (3), 380-387. https://doi.org/10.1017/S1446788700024939