DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Dong-Su | - |
dc.contributor.advisor | 김동수 | - |
dc.contributor.author | Shin, Hee-Sung | - |
dc.contributor.author | 신희성 | - |
dc.date.accessioned | 2011-12-14T04:40:12Z | - |
dc.date.available | 2011-12-14T04:40:12Z | - |
dc.date.issued | 2007 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=268707&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41898 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2007. 8, [ v, 42 p. ] | - |
dc.description.abstract | A $\emph{leader}$ 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.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | refinement | - |
dc.subject | numbers | - |
dc.subject | trees | - |
dc.subject | parking functions | - |
dc.subject | 세분화 | - |
dc.subject | 개수 | - |
dc.subject | 수형도 | - |
dc.subject | 주차 함수 | - |
dc.subject | refinement | - |
dc.subject | numbers | - |
dc.subject | trees | - |
dc.subject | parking functions | - |
dc.subject | 세분화 | - |
dc.subject | 개수 | - |
dc.subject | 수형도 | - |
dc.subject | 주차 함수 | - |
dc.title | A refinement of numbers for trees and parking functions | - |
dc.title.alternative | 수형도와 주차 함수의 개수에 대한 세분화 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 268707/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020015159 | - |
dc.contributor.localauthor | Kim, Dong-Su | - |
dc.contributor.localauthor | 김동수 | - |
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