Matroids related to groups and semigroups

D.I. Bezushchak (Taras Shevchenko National University of Kyiv)

Abstract


Matroid is defined as a pair $$$(X,\mathcal{I})$$$, where $$$X$$$ is a nonempty finite set, and $$$\mathcal{I}$$$ is a nonempty set of subsets of  $$$X$$$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $$$S$$$, the pair $$$(\widehat{S}, \mathcal{I})$$$ will be a matroid.

Keywords


semigroup; matroid

MSC 2020


20M75; 20M99

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References


Aigner M. Combinatorial Theory, Springer Verlag, 1996.

Clifford A.H., Preston G.B. The Algebraic Theory of Semigroups. Vol. I., American Math. Soc., 1961.

Neel D.L., Neudauer N.A. "Matroids you have known", Mathematics Magazine, 2009; 82(1): pp. 26-41. doi:10.4169/193009809X469020

Wilson Robin J. Introduction to Graph Theory, Longman, 2010.




DOI: https://doi.org/10.15421/242309

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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