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A refinement for ordered labeled trees
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Let On be the set of ordered labeled trees on {0; : : : ; n}. A maximal decreasing subtree of an ordered labeled tree is de ned by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new re nement On;k of On,which is the set of ordered labeled trees whose maximal decreasing subtree has k + 1 vertices.
Abstract
Let On be the set of ordered labeled trees on {0; : : : ; n}. A maximal decreasing subtree of an ordered labeled tree is de ned by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new re nement On;k of On,which is the set of ordered labeled trees whose maximal decreasing subtree has k + 1 vertices.
참고문헌 (8)
- William Y. C. Chen, "Recurrence relations for strongly q-log-convex polynomial", Canad. Math. Bull, 54(2), pp.217~229 (2011)
- Brian Drake, "An inversion theorem for labeled trees and some limits of areas under lattice paths", 박사, pp.2008
- Martin Klazar, "Twelve countings with rooted plane trees", European J. Combin, 18(2), pp.195~210 (1997)
- 신희성, "A generalized enumeration of labeled trees and reverse Prufer algorithm", JOURNAL OF COMBINATORIAL THEORY SERIES A, 114(7), pp.1357~1361, ACADEMIC PRESS INC ELSEVIER SCIENCE
- 신희성, "On the enumeration of rooted trees with fixed size of maximal decreasing trees", DISCRETE MATHEMATICS, 312(2), pp.419~426, ELSEVIER SCIENCE BV
- Peter W. Shor, "A new proof of Cayley's formula for counting labeled trees", J. Combin. Theory Ser. A, 71(1), pp.154~158 (1995)
- Richard P. Stanley, "Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics" (1999), Cambridge University Press
- Jiang Zeng, "A Ramanujan sequence that renes the Cayley formula for trees", Ramanujan J., 3(1), pp.45~54 (1999)
관련 논문AI추천
A REFINED ENUMERATION OF p-ARY LABELED TREES서승현, 신희성강원경기수학회 · 한국수학논문집2013 · 제21권 제4호Refined enumeration of vertices among all rooted ordered $d$-trees김상욱, 서승현, 신희성대한수학회 · 대한수학회보2019 · 제56권 제4호Pick two points in a tree김하나, Louis W. Shapiro대한수학회 · 대한수학회지2019 · 제56권 제5호HYBRID d-ARY TREES AND THEIR GENERALIZATION박승경, 홍성지대한수학회 · 대한수학회보2014 · 제51권 제1호Enumeration of optimally labelled graphs of bandwidth 2김상목, 정민석, 채갑병대한수학회 · 대한수학회보2017 · 제54권 제6호The Number of Independent Dominating Sets of Labeled TreesChangwoo Lee대한수학회 · 대한수학회논문집2003 · 제18권 제1호
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