Properties of Graded Posets Preserved by Some Operations
We answer the following question: Let P and Q be graded posets having some property and let ∘ be some posets operation. Is it true that P ∘ Q has also this property? The considered properties are: being Sperner, a symmetric chain order, Peck, LYM, and rank compressed. The studied operations are: direct product, direct sum, ordinal sum, ordinal product, rankwise direct product, and exponentiation.
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