Chih-wen Weng

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A pooling space is defined to be a ranked partially ordered set with atomic intervals. We show how to construct non-adaptive pooling designs from a pooling space. Our pooling designs are e-error detecting for some e; moreover e can be chosen to be very large compared with the maximal number of defective items. Eight new classes of nonadaptive pooling(More)
We show that the quantum algebra Uq(sl2) has a presentation with generators x±1, y, z and relations xx−1 = x−1x = 1, qxy − q−1yx q − q−1 = 1, qyz − q−1zy q − q−1 = 1, qzx − q−1xz q − q−1 = 1. We call this the equitable presentation. We show that y (resp. z) is not invertible in Uq(sl2) by displaying an infinite dimensional Uq(sl2)-module that contains a(More)
Brouwer, Cohen, and Neumaier found that the intersection numbers of most known families of distance-regular graphs could be described in terms of four parameters (d, b, :, ;) [2, pp. ix, 193]. They invented the term classical to describe those graphs for which this could be done. All classical distance-regular graphs with b=1 are classified by Y. Egawa, A.(More)
Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1 ≤ k − a1 − c2 c2 − 1 . We show the following (i)–(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph(More)
A superimposed code with general distance D can be used to construct a non-adaptive pooling design. It can then be used to identify a few unknown positives from a large set of items by associating naturally an outcome vector u. A simple method for decoding the outcome vector u is given whenever there are at most bD−1 2 c errors occuring in the outcome(More)
Let G = (V G,EG) be a connected graph on n vertices, with diameter D, adjacency matrix A, and distance function ∂. Assume that A has d + 1 distinct eigenvalues λ0 > λ1 > · · · > λd with corresponding multiplicities m0 = 1, m1, . . ., md. From the spectrum of G we then define an inner product 〈·, ·〉4 on the vector space Rd[x] of real polynomials of degree at(More)
We study partially distance-regular graphs and partially walkregular graphs as generalizations of distance-regular graphs and walkregular graphs respectively. We conclude that the partially distanceregular graphs can be viewed as some extremal graphs of partially walk-regular graphs. In the special case that the graph is assumed to be regular with four(More)
Let Γ = (X, R) denote a distance-regular graph with distance function ∂ and diameter d ≥ 3. For 2 ≤ i ≤ d, by a parallelogram of length i, we mean a 4-tuple xyzu of vertices in X such that ∂(x, y) = ∂(z, u) = 1, ∂(x, u) = i, and ∂(x, z) = ∂(y, z) = ∂(y, u) = i − 1. Suppose the intersection number a1 = 0, a2 6= 0 in Γ. We prove the following (i)-(ii) are(More)