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The Specht ideal of shape $\lambda$, where $\lambda$ is a partition, is theideal generated by all Specht polynomials of shape $\lambda$. Haiman and Wooproved that these ideals are reduced and found their universal Gr\"obner bases.In this short note, we give a short proof for these results.

A note on the reducedness and Gr\"obner bases of Specht ideals