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组合几何中一类填充与覆盖问题的研究 ...
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201310.6482v3 Algebraic combinatorial geometry - the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory [代数组合几何:算术组合学、关联组合学及数论中的多项式方法].pdf
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry is often concerned with the problem of bounding the behaviour of arbitrary finite collections of geometric objects such as points, lines, or circles with respect to geometric operations such as incidence or distance. Given the presence of arbitrary finite sets in these problems, the methods used to attack these problems have primarily been combinatorial in nature. In recent years, however, many outstanding problems in these questions have been solved by algebraic means (and more specifically, using tools from algebraic geometry and/or algebraic topology), giving rise to an emerging set of techniques which is now known as the polynomial method.
While various instances of the polynomial method have been known for decades (e.g. Step
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向豆丁求助:有没有组合几何?