Journal
ACTA MATHEMATICA SCIENTIA
Volume 41, Issue 1, Pages 97-113Publisher
SPRINGER
DOI: 10.1007/s10473-021-0106-4
Keywords
Hilbert Problem 15; enumeration geometry; incidence formula
Categories
Funding
- National Center for Mathematics and Interdisciplinary Sciences, CAS
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This paper proves the correctness of formulas regarding the incidence of points, lines, and planes in sections 6, 7, and 10, following the ideas presented in Schubert's book. Additionally, formulas 8 and 9 in section 12, which are frequently used in the book, are also proven as an application.
Hilbert Problem 15 required an understanding of Schubert's book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in 6, 7, 10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in 12, which are frequently used in his book.
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