Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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REFINED ENUMERATION OF VERTICES AMONG ALL ROOTED ORDERED d-TREES

  • Kim, Sangwook (Department of Mathematics Chonnam National University) ;
  • Seo, Seunghyun (Department of Mathematics Education Kangwon National University) ;
  • Shin, Heesung (Department of Mathematics Inha University)
  • Received : 2018.07.12
  • Accepted : 2018.12.10
  • Published : 2019.07.31
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Abstract

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

Keywords

E1BMAX_2019_v56n4_899_f0001.png 이미지

FIGURE 1. All rooted 3-tuplet trees with 3 tuplets in $T ^{(3)}_3$

E1BMAX_2019_v56n4_899_f0002.png 이미지

FIGURE 2. Two bijections $\varphi$ and $\overline{\varphi}$

E1BMAX_2019_v56n4_899_f0003.png 이미지

FIGURE 3. The bijection ψ

E1BMAX_2019_v56n4_899_f0004.png 이미지

FIGURE 4. Tree decomposition

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FIGURE 5. Outline of a lattice path P induced from tree decomposition

E1BMAX_2019_v56n4_899_f0006.png 이미지

FIGURE 6. Cut-and-paste bijection γi,j

TABLE 1. The number of vertices of outdegree k at level l among all rooted 3-tuplet trees in $T ^{(3)}_3$

E1BMAX_2019_v56n4_899_t0001.png 이미지

References

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