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Award ID contains: 1720335

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  1. ; ; ; ; (, Advances in Applied Mathematics)
    null (Ed.)
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  2. ; (, Association for Women in Mathematics series)
    In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Groebner bases for the ideal of the data points. While the theory of Groebner bases is extensive, what is missing is a closed form for their number for a given ideal. This work contributes connections between the geometry of data points and the number of Groebner bases associated to small data sets. Furthermore we improve an existing upper bound for the number of Groebner bases specialized for data over a finite field. 
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  3. ; ; ; (, Journal of Algebra and Its Applications)
    In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Gröbner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Gröbner bases, that is, with the same cardinality of their associated Gröbner fan. 
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  4. ; ; ; (, Bulletin of Mathematical Biology)
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