Counting ternary trees according to the number of middle edges and factorizing into (3/2)-ary trees

2020/09/14 by Helmut Prodinger, Prodinger, Helmut
Computer Science · #Advanced Graph Theory Research #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2009.06793

openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The sequence A120986 in the Encyclopedia of Integer Sequences counts ternary trees according to the number of nodes and the number of middle edges. Using a certain substition, the underlying cubic equation can be factored. This leads to an extension of the concept of (3/2)-ary trees, introduced by Knuth in his christmas lecture from 2014.

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