In an approach to the Cayley formula for counting trees, Shor discovered a refined recurrence relation concerning the number of improper edges. Chen and the author gave a bijection for the Shor recurrence based on the combinatorial interpretations of Zeng, answering a question of Shor. In this paper, we present a new bijective proof of the Shor recurrence by applying Shor's formula for counting forests of rooted trees with roots 1, . . . , r and with a given number of improper edges. (C) 2017 Elsevier Ltd. All rights reserved.
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