Evaluations of the circuit partition polynomial

Abstract

J. A. Ellis-Monaghan (1998, J. Combin. Theory Ser. B 74, 326-352) used Hopf algebra techniques to prove some beautiful combinatorial interpretations of the Martin polynomial for unoriented graphs. Our aim here is to give very simple proofs of similar interpretations for a considerably wider class of values. The results look particularly simple when formulated for a trivial transform of the Martin polynomial, the circuit partition polynomial. © 2002 Elsevier Science (USA).