The Fröberg conjecture and some questions on powers of general linear forms

Abstract: The longstanding Fröberg conjecture states that there are no non-trivial relations between general homogeneous polynomials. But if we replace "general homogeneous polynomials" by ”powers of general linear forms” it turns out that in some cases there are in fact such non-trivial relations, which may at first seem unnatural. I will present some results and some combinatorial questions related to these two classes of objects, and will give brief connections to lattice paths, the Exterior algebra, the Lefschetz properties, and fat point schemes. No previous knowledge of the Fröberg conjecture is assumed.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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