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Transversal and cotransversal matroids via their representations.
 

Summary: Transversal and cotransversal matroids
via their representations.
Federico Ardila
Submitted: May 23, 2006; Accepted: Feb. 27, 2007
Mathematics Subject Classification: 05B35; 05C38; 05A99
Abstract.
It is known that the duals of transversal matroids are precisely the strict gammoids.
We show that, by representing these two families of matroids geometrically, one
obtains a simple proof of their duality.
0
This note gives a new proof of the theorem, due to Ingleton and Piff [3], that the duals
of transversal matroids are precisely the strict gammoids. Section 1 defines the relevant
objects. Section 2 presents explicit representations of the families of transversal matroids
and strict gammoids. Section 3 uses these representations to prove the duality of these
two families.
1
Matroids and duality. A matroid M = (E, B) is a finite set E, together with a non-empty
collection B of subsets of E, called the bases of M, which satisfy the following axiom: If
B1, B2 are bases and e is in B1 - B2, there exists f in B2 - B1 such that (B1 - e) f is
a basis.

  

Source: Ardila, Federico - Department of Mathematics, San Francisco State University

 

Collections: Mathematics