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math.AC2018★ 6 cited
Free extensions and Lefschetz properties, with an application to rings of relative coinvariants
Chris McDaniel, Shujian Chen, Anthony Iarrobino +1
Graded Artinian algebras can be regarded as algebraic analogues of cohomology rings (in even degrees) of compact topological manifolds. In this analogy, a free extension of a base…
math.MG2018
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…