The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids
Abstract
We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we show that the foundation of a 2-sum of matroids is the absolute tensor product of the foundations, and that the foundation of a matroid is invariant under segment-cosegment exchange.Mathematics Subject Classifications: 05B35, 20AxxKeywords: Matroids, pastures, foundations, generalized parallel connection, 2-sum, segment-cosegment exchange
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Graph Theory Research
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- Combinatorial Theory
- Volume
- 5
- Issue
- 4
- Publication date
- 2 February 2026