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Perfect Solutions to Problems on Common Transversals and Submodular Functions from Welsh’s 1976 Text Matroid Theory

Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1
DOI:
https://doi.org/10.1556/314.2022.00023
Author:
Jonathan David Farley

Problem 2 of Welsh’s 1976 text Matroid Theory, asking for criteria telling when two families of sets have a common transversal, is solved.

Another unsolved problem in the text Matroid Theory, on whether the “join” of two non-decreasing submodular functions is submodular, is answered in the negative. This resolves an issue first raised by Pym and Perfect in 1970.

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