The authors compute Gröbner bases for ideals (x₁²,…,xₙ²,(x₁+⋯+xₙ)^k), classify their weak Lefschetz properties via combinatorial structures, and prove the strong Lefschetz property for the squarefree algebra.
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Gr\"obner bases, resolutions, and the Lefschetz properties for powers of a general linear form in the squarefree algebra
The authors compute Gröbner bases for ideals (x₁²,…,xₙ²,(x₁+⋯+xₙ)^k), classify their weak Lefschetz properties via combinatorial structures, and prove the strong Lefschetz property for the squarefree algebra.