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Bull. Korean Math. Soc. 2019; 56(4): 899-910

Online first article July 9, 2019      Printed July 31, 2019

https://doi.org/10.4134/BKMS.b180661

Copyright © The Korean Mathematical Society.

Refined enumeration of vertices among all rooted ordered $d$-trees

Sangwook Kim, Seunghyun Seo, Heesung Shin

Chonnam National University; Kangwon National University; Inha University

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In this paper, we enumerate the cardinalities for the set of all vertices of outdegree $\ge k$ at level $\ge \ell$ among all rooted ordered $d$-trees with $n$ edges. Our results unite and generalize several previous works in the literature.

Keywords: rooted ordered $d$-tree, lattice path, bijection, degree, level

MSC numbers: 05A15

Supported by: For the second author, this research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2017R1D1A1B03033276). For the third author, this work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP)(NRF-2017R1C1B2008269)

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