2020
DOI: 10.1080/10586458.2020.1740835
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Probabilistic Saturations and Alt’s Problem

Abstract: Alt's problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as counting the number of solutions to a system of polynomial equations which was first solved numerically using homotopy continuation by Wampler, Morgan, and Sommese in 1992. Since there is still not a proof that all solutions were obtained, we consider upper bounds for Alt's problem by counting the number of solutions outside of the base… Show more

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Cited by 3 publications
(1 citation statement)
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“…In each case, showing that the scheme is irreducible and reduced is now equivalent to showing that the top-dimensional irreducible component has the same Hilbert series as the entire scheme; this precludes the existence of embedded components. This was verified using [6] with certified numerical Hilbert function computations [12]. In fact, this also showed that each scheme is arithmetically Cohen-Macaulay.…”
Section: Introductionmentioning
confidence: 59%
“…In each case, showing that the scheme is irreducible and reduced is now equivalent to showing that the top-dimensional irreducible component has the same Hilbert series as the entire scheme; this precludes the existence of embedded components. This was verified using [6] with certified numerical Hilbert function computations [12]. In fact, this also showed that each scheme is arithmetically Cohen-Macaulay.…”
Section: Introductionmentioning
confidence: 59%