Browsing by Author "Huang, Hau-wen"

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More on pooling spaces
(2008-12-28)
Huang, Hau-wen
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Huang, Yu-pei
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Weng, Chih-wen
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應用數學系
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Department of Applied Mathematics
A pooling space is a ranked poset P such that the subposet w(+) induced by the elements above w is atomic for each element w of P. Pooling spaces were introduced in IT. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Math. 282 (2004) 163-169] for the purpose of giving a uniform way to construct pooling designs, which have applications to the screening of DNA sequences. Many examples of pooling spaces were given in that paper. In this paper, we clarify a few things about the definition of pooling spaces. Then we find that a geometric lattice, a well-studied structure in literature, is also a pooling space. This provides us many classes of pooling designs, some old and some new. We study the pooling designs constructed from affine geometries. We find that some of them meet the optimal bounds related to a conjecture of Erdos, Frankl and Furedi. (c) 2007 Elsevier B.V. All rights reserved.
The classification of Leonard triples of QRacah type
(2012-03-01)
Huang, Hau-wen
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應用數學系
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Department of Applied Mathematics
Let K denote an algebraically closed field. Let V denote a vector space over K with finite positive dimension. By a Leonard triple on V we mean an ordered triple of linear transformations in End(V) such that for each of these transformations there exists a basis of V with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal. There is a family of Leonard triples said to have QRacah type. This is the most general type of Leonard triple. We classify the Leonard triples of QRacah type up to isomorphism. We show that any Leonard triple of QRacah type satisfies the Z(3)-symmetric Askey-Wilson relations. (C) 2011 Published by Elsevier Inc.
The edge-flipping group of a graph
(2010-04-01)
Huang, Hau-wen
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Weng, Chih-wen
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應用數學系
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Department of Applied Mathematics
Let X = (V, E) be a finite simple connected graph with it vertices and In edges A configuration is all assignment of one of the two colors, black or white, to each edge of X. A move applied to a configuration is to select a black edge c c E and change the colors of all adjacent edges off Given all Initial Configuration and a filial Configuration, try to find a sequence of moves that transforms the Initial Configuration into the final configuration This is rile edge-flipping puzzle oil X, and it corresponds to a group action This group is called the edge-flipping group W(E)(X) of X This paper shows that if X has at least three vertices. W(r)(X) is isomorphic to a semidirect product of (Z/2Z)(k) and the symmetric group S(n) of degree n, where k = (n - 1)(m - n + 1) if n is odd, k = (n - 2)(m - n + 1) if n is even, and Z is the additive group of integers (C) 2009 Elsevier Ltd All rights reserved.
The flipping puzzle on a graph
(2010-08-01)
Huang, Hau-wen
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Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let S be a connected graph which contains an induced path of n - 1 vertices, where n is the order of S. We consider a puzzle on S. A configuration of the puzzle is simply an n-dimensional column vector over {0, 1} with coordinates of the vector indexed by the vertex set S. For each configuration u with a coordinate u(s) = 1, there exists a move that sends u to the new configuration which flips the entries of the coordinates adjacent to s in u. We completely determine if one configuration can move to another in a sequence of finite steps. (C) 2010 Published by Elsevier Ltd