Abstract. The spanning tree invariant of Lind and Tuncel is observed in the context of loop systems of Markov chains. For n = 1, 2, 3 the spanning tree invariants of the loop systems of a Markov chain determined by an irreducible stochastic (n x n)-matrix P coincide if and only if P is doubly stochastic and, in this case, the common value of the spanning tree invariants of the loop systems is n.

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