http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
- 中文 을 입력하시려면 zhongwen을 입력하시고 space를누르시면됩니다.
- 北京 을 입력하시려면 beijing을 입력하시고 space를 누르시면 됩니다.
RISS 인기검색어
- 검색키워드
- 저자 : Louis W. Shapiro (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
-
Louis W. Shapiro,김하나 대한수학회 2019 대한수학회지 Vol.56 No.5
In ordered trees, two randomly chosen vertices are said to be dependent if one lies under the other. If not, we say that they are independent. We consider several classes of ordered trees with uniform updegree requirements and find the generating functions for the trees with two marked dependent/independent vertices. As a result, we compute the probability for two vertices being dependent/independent. We also count such trees by the distance between two independent vertices.
-
A link between ordered trees and Green-Red trees
천기상,김하나,Louis W. Shapiro 대한수학회 2016 대한수학회지 Vol.53 No.1
The $r$-ary number sequences given by $$(\mathfrak{b}_{n}^{(r)})_{n\ge0} ={\frac{1}{(r-1)n+1}}{\binom{rn}{n}}$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}{\binom{2n}{n}}$. Their history goes back at least to Lambert \cite{BLam} in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various $r$ first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give $r$-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $\mathfrak{b}_n^{(r)}$ and $\mathfrak{b}_n^{(r+1)}$.
-
Kim, Hana,Shapiro, Louis W. Korean Mathematical Society 2019 대한수학회지 Vol.56 No.5
In ordered trees, two randomly chosen vertices are said to be dependent if one lies under the other. If not, we say that they are independent. We consider several classes of ordered trees with uniform updegree requirements and find the generating functions for the trees with two marked dependent/independent vertices. As a result, we compute the probability for two vertices being dependent/independent. We also count such trees by the distance between two independent vertices.
-
Cheon, Gi-Sang,Lee, Sang-Gu,Shapiro, Louis W. Elsevier 2010 European journal of combinatorics : Journal europ& Vol.31 No.1
<P><B>Abstract</B></P><P>We give a short combinatorial proof of a Fine number generating function identity and then explore some of the ramifications in terms of random walks, friendly walkers, and ordered trees. The results are also generalized to obtain similar results including those in Motzkin and Schröder settings.</P>
연관 검색어 추천
이 검색어로 많이 본 자료
활용도 높은 자료
