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Abstract for D. Fon-Der-Flaass, Local equivalence of transversals in matroids

Given any system of $n$ subsets in a matroid $M$, a {\it transversal}
of this system is an $n$-tuple of elements of $M$, one from each set,
which is independent. Two transversals differing by exactly one element
are adjacent, and two transversals connected by a sequence of adjacencies
are {\it locally equivalent}, the distance between them being the minimum 
number of adjacencies in such a sequence. 

We give two sufficient conditions for all transversals of a set system 
to be locally equivalent. Also we propose a conjecture that the distance 
between any two locally equivalent transversals can be bounded by a function 
of $n$ only, and provide an example showing that such function, 
if it exists, must grow at least exponentially.


\bye

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