Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1

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

Author:
Jonathan David Farley Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, United States of America

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Pages:
8–16
Online Publication Date:
14 Oct 2022
Publication Date:
19 May 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2022.00023
Keywords:
Independence space; independence structure; matroid; submodular; (common) transversal
Open access

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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Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
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  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
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Issues
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ISSN 2786-0752 (Online)
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