A refinement of numbers for trees and parking functions = 수형도와 주차 함수의 개수에 대한 세분화

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dc.contributor.advisorKim, Dong-Su-
dc.contributor.advisor김동수-
dc.contributor.authorShin, Hee-Sung-
dc.contributor.author신희성-
dc.date.accessioned2011-12-14T04:40:12Z-
dc.date.available2011-12-14T04:40:12Z-
dc.date.issued2007-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=268707&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41898-
dc.description학위논문(박사) - 한국과학기술원 : 수리과학과, 2007. 8, [ v, 42 p. ]-
dc.description.abstractA $\emph{leader}$ of a tree $T$ is a vertex which has no smaller descendants in $T$. Gessel and Seo showed that $\displaystyle\sum_{T \in T_n}u^{(\# of leaders in T)}c^{(degree of 1 in T)} = u P_{n-1}(1,u,cu),$ which is a generalization of Cayley``s formula, where $T_n$ is the set of trees on $[n]$ and $P_n(a,b,c) = c \displaystyle\prod_{i=1}^{n-1}(ia+(n-i)b+c).$ Using a variation of the Pr$\ddot{u}$fer code which is called an $\em{RP-code}$, we give a simple bijective proof of Gessel and Seo``s formula. A car in a parking function is called $\emph{lucky}$ if it succeeds to park in its preferred space. Gessel and Seo also showed that $\displaystyle\sum_{P \in PF_n} u^{(\# of lucky cars in P)} = P_n(1,u,u),$ but this proof was not combinatorial. We construct the bijection $\varphi$ from forests to parking functions and give a bijective proof of it. We generalize it further using the bijection $\varphi$.eng
dc.languageeng-
dc.publisher한국과학기술원-
dc.subjectrefinement-
dc.subjectnumbers-
dc.subjecttrees-
dc.subjectparking functions-
dc.subject세분화-
dc.subject개수-
dc.subject수형도-
dc.subject주차 함수-
dc.subjectrefinement-
dc.subjectnumbers-
dc.subjecttrees-
dc.subjectparking functions-
dc.subject세분화-
dc.subject개수-
dc.subject수형도-
dc.subject주차 함수-
dc.titleA refinement of numbers for trees and parking functions = 수형도와 주차 함수의 개수에 대한 세분화-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN268707/325007 -
dc.description.department한국과학기술원 : 수리과학과, -
dc.identifier.uid020015159-
dc.contributor.localauthorKim, Dong-Su-
dc.contributor.localauthor김동수-
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