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Eberly College of Arts and Sciences




A rational function of the form x α1 1 x α2 2 ⋯x αn n x β1 1 +x β2 2 +⋯+x βn n is a Genocchi-Peano example, GPE, provided it is discontinuous, but its restriction to any hyperplane is continuous. We show that the minimal degree D(n) of a GPE of n-variables equals 2 ⌊ e 2 e2−1 n⌋ + 2i for some i ∈ {0, 1, 2}. We also investigate the minimal degree Db(n) of a bounded GPE of n-variables and note that D(n) ≤ Db(n) ≤ n(n + 1). Finding better bounds for numbers Db(n) remains an open problem.

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Mathematics Commons



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