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A REFINED ENUMERATION OF p-ARY LABELED TREES
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Let Tn(p) be the set of p-ary labeled trees on ｛1, 2, . . . , n｝. A maximal decreasing subtree of an p-ary labeled tree is de ned bythe maximal p-ary subtree from the root with all edges being de-creasing. In this paper, we study a new re nement Tn,k(p)n of Tn(p),which is the set of p-ary labeled trees whose maximal decreasingsubtree has k vertices.
Abstract
Let Tn(p) be the set of p-ary labeled trees on ｛1, 2, . . . , n｝. A maximal decreasing subtree of an p-ary labeled tree is de ned bythe maximal p-ary subtree from the root with all edges being de-creasing. In this paper, we study a new re nement Tn,k(p)n of Tn(p),which is the set of p-ary labeled trees whose maximal decreasingsubtree has k vertices.
참고문헌 (6)
- Francois Bergeron, "Philippe Flajolet, and Bruno Salvy, Varieties of increasing trees, In CAAP '92 (Rennes, 1992)", Lecture Notes in Comput. Sci., 581, pp.24~48 (1992), Springer
- Ronald L. Graham, "Concrete mathematics, In A foundation for computer science" (1989), Addison-Wesley Publishing Company Advanced Book Program
- Seunghyun Seo, "A generalized enumeration of labeled trees and reverse Prufer algorithm", J. Combin. Theory Ser. A, 114(7), pp.1357~1361 (2007)
- Seunghyun Seo, "On the enumeration of rooted trees with fixed size of maximal decreasing trees", Discrete Math, 312(2), pp.419~426 (2012)
- 서승현, "A refinement for ordered labeled trees", 한국수학논문집, 20(2), pp.255~261 (2012), 강원경기수학회[DOI]
- Richard P. Stanley, "Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics" (1999), Cambridge University Press, Cam- bridge
관련 논문AI추천
A refinement for ordered labeled trees서승현, 신희성강원경기수학회 · 한국수학논문집2012 · 제20권 제2호Refined enumeration of vertices among all rooted ordered $d$-trees김상욱, 서승현, 신희성대한수학회 · 대한수학회보2019 · 제56권 제4호HYBRID d-ARY TREES AND THEIR GENERALIZATION박승경, 홍성지대한수학회 · 대한수학회보2014 · 제51권 제1호Pick two points in a tree김하나, Louis W. Shapiro대한수학회 · 대한수학회지2019 · 제56권 제5호Enumeration of optimally labelled graphs of bandwidth 2김상목, 정민석, 채갑병대한수학회 · 대한수학회보2017 · 제54권 제6호Enumeration of graphs with given weighted number of connected components송정민대한수학회 · 대한수학회보2017 · 제54권 제6호
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