• East Asian mathematical journal
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• 제31권5호
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• 대한수학회지
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• 제52권6호
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• pp.1123-1137
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• 2015

We study colorings of regular trees using subball complexity b(n), which is the number of colored n-balls up to color-preserving isomorphisms. We show that for any k-regular tree, for k > 1, there are colorings of intermediate complexity. We then construct colorings of linear complexity b(n) = 2n + 2. We also construct colorings induced from sequences of linear subword complexity which has exponential subball complexity.

• 대한수학회지
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• 제37권3호
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• pp.473-490
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• 2000

Removal independence is a translation of Arrow's axiom of independence of irrelevant alternatives for social welfare functions to an axiom about consensus functions involving n-trees. It is shown that a consensus function is removal independent if and only if it is expressible as th union of three types of functions.

• Korean Journal of Mathematics
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• 제20권2호
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• pp.255-261
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• 2012

Let $\mathcal{O}_n$ be the set of ordered labeled trees on $\{0,\;{\ldots},\;n\}$. A maximal decreasing subtree of an ordered labeled tree is defined by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{O}_{n,k}$ of $\mathcal{O}_n$, which is the set of ordered labeled trees whose maximal decreasing subtree has $k+1$ vertices.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.495-502
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• 2013

Let $\mathcal{T}^{(p)}_n$ be the set of p-ary labeled trees on $\{1,2,{\ldots},n\}$. A maximal decreasing subtree of an p-ary labeled tree is defined by the maximal p-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{T}^{(p)}_{n,k}$ of $\mathcal{T}^{(p)}_n$, which is the set of p-ary labeled trees whose maximal decreasing subtree has k vertices.

• 한국멀티미디어학회논문지
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• 제13권12호
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• pp.1760-1766
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• 2010

The linearized suffix tree (LST) is an array data structure supporting traversals on suffix trees. We apply this LST to two dimensional (2D) suffix trees and obtain a space-efficient substitution of 2D suffix trees. Given an $n{\times}n$ text matrix and an $m{\times}m$ pattern matrix over an alphabet ${\Sigma}$, our 2D-LST provides pattern matching in $O(m^2log{\mid}{\Sigma}{\mid})$ time and $O(n^2)$ space.

• 한국정보과학회논문지:시스템및이론
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• 제27권2호
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• pp.209-215
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• 2000

본 논문에서는 n개의 노드로 이루어진 이진트리를 평면에 그리는 한 방법인 평면 다각선 상향 순서보존 그리드 방법을 이용하여 높이 0(n), 폭 0(log n), 면적 O(n log n)은 기존의 결과와 같게 유지하면서, 굴곡점의 수를 (n)에서 (n/logn)으로 줄이는 알고리즘을 제시한다.

• 대한수학회지
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• 제53권1호
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• pp.187-199
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• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] 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 $b^{(r)}_n$ and $b^{(r+1)}_n$.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.639-647
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• 2005

We count the number of maximal independent sets of binary trees and planted plane trees.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.471-474
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• 1998

In this paper, we consider the problem of optimal broadcasting in recursive circulants under multi-port communication model. Recursive circulant G(N, d) that is defined to be a circulant graph with N vertices and jumps of powers of d is a useful interconnection network from the viewpoint of network metrices. Our model assumes that a processor can transmit a message to $\alpha$ neighboring processors simultaneously where $\alpha$ is two or three. For the broadcasting problem, we introduce 3-trees and 4-trees. And then we show that 3-trees and 4-trees are minimum broadcast trees in 2-port model and 3-port model. Using the above results, we show that recursive circulants g(2m, 2) have optimum broadcasting time in 2-port model and 3-port model.