Refined enumeration of vertices among all rooted ordered $d$-trees
Bull. Korean Math. Soc. 2019 Vol. 56, No. 4, 899-910
Published online July 9, 2019
Printed July 31, 2019
Sangwook Kim, Seunghyun Seo, Heesung Shin
Chonnam National University; Kangwon National University; Inha University
Abstract : 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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