In this paper we examine the enumeration of alternating trees. We give a bijective proof of the fact that the number of alternating unrooted trees with n vertices is given by (12(n-1)) Sigma (n)(k=1) ((n)(k))k(n-1), a problem first posed by A. Postnikov (1997. J. Combin. Theory Ser. A 79, 360-366). We also show that the number of alternating ordered trees with n vertices is 2(n - 1)(n-1). (C) 2001 Academic Press. [References: 6]
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