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Activity Number:
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34
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Type:
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Contributed
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Date/Time:
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Sunday, August 6, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #305650 |
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Title:
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A Catalog of Nonisomorphic Indicator Functions
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Author(s):
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Shao-Wei Cheng*+ and Chien-Yu Peng
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Companies:
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Academia Sinica and Academia Sinica
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Address:
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Institute of Statistical Science, Taipei, 115, Taiwan
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Keywords:
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factorial designs ; index sets ; j-characteristics
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Abstract:
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The indicator function of a design A is a polynomial function defined on the design space D such that for each design point x in D, the value of the function is the number of appearances of x in A. For nonregular designs, indicator function plays a role similar to defining contrast subgroup in regular designs. We characterize an indicator function as a combination of two key elements---the index set of monomials with nonzero coefficients and the values of these coefficients---from which the concept of isomorphism for indicator functions is developed. We link the nonzero coefficients and their corresponding contrasts to a system of linear equations whose structure is related to a regular design. By solving different sets of linear equations, a catalog of nonisomorphic indicator functions can be constructed. We will present a catalog obtained from an exhausted computer search.
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