A bijective proof of the Shor recurrence. (May 2018)

• Record Type: Journal Article
• Authors: Guo, Victor J.W.
• Is Part Of: European journal of combinatorics. Volume 70(2018)
• Page Start: 92
• Page End: 98
• Publication Date: 2018-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2017.12.004
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: 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.