Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property

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Publication:3967539

DOI10.1137/0601021zbMath0502.05004OpenAlexW1981696777MaRDI QIDQ3967539

Richard P. Stanley

Publication date: 1980

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0601021



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Cites Work