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

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

Event Category:

Discrete Math Seminar

Speaker:
Jonathan Farley

Institution:
Morgan State University

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.

Friday, April 7, 2023 - 2:30pm

LGRT 1528

## Department of Mathematics and Statistics