Abstract
AbstractMallows and Riordan “The Inversion Enumerator for Labeled Trees,” Bulletin of the American Mathematics Society, vol. 74 [1968] pp. 92‐94) first defined the inversion polynomial, Jn(q) for trees with n vertices and found its generating function. In the present work, we define inversion polynomials for ordered, plane, and cyclic trees, and find their values at q = 0, ± 1. Our techniques involve the use of generating functions (including Lagrange inversion), hypergeometric series, and binomial coefficient identities, induction, and bijections. We also derive asymptotic formulae for those results for which we do not have a closed form. © 1995 John Wiley & Sons, Inc.
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