A partition matroid is a matroid obtained from a set partition 
of its finite ground set 
and nonnegative
integers 
. A subset 
is independent precisely when
for each
(van Bevern et al. 2021, Garami
2026).
Partition Matroid
See also
Ground Set, Matroid, Matroid Coloring, Matroid Intersection, Set PartitionExplore with Wolfram|Alpha
References
Garami, B. "A Note on the List Chromatic Number of Two Matroids." 5 Oct 2026. https://arxiv.org/abs/2610.07318.van Bevern, R.; Tsidulko, O. Yu.; and Zschoche, P. "Representative Families for Matroid Intersections, with Applications to Location, Packing, and Covering Problems." Disc. Appl. Math. 298, 110-128, 2021. https://doi.org/10.1016/j.dam.2021.03.014.Cite this as:
Weisstein, Eric W. "Partition Matroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PartitionMatroid.html