논문KCI 등재
Refined enumeration of vertices among all rooted ordered $d$-trees
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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.
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.
참고문헌 (6)
- L. W. Beineke, "The number of labeled k-dimensional trees", J. Combi-natorial Theory, 6, pp.200~205 (1969)
- Miklós Bóna, "Enumeration of m-Ary Cacti", Advances in Applied Mathematics, 24(1), pp.22~56 (2000), Elsevier BV[DOI]
- Sen-Peng Eu, "Enumerations of vertices among all rooted ordered trees with levels and degrees", Discrete Mathematics, 340(9), pp.2123~2129 (2017), Elsevier BV[DOI]
- F. Harary, "On the Number of Husimi Trees: I", Proceedings of the National Academy of Sciences, 39(4), pp.315~322 (1953), Proceedings of the National Academy of Sciences[DOI]
- Mahendra Jani, "Enumeration of K-Trees and Applications", Annals of Combinatorics, 6(3), pp.375~382 (2002), Springer Science and Business Media LLC[DOI]
- S. Seo, "Two involutions on vertices of ordered trees. I", 14st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2002) (2002)
관련 논문AI추천
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