Abstract
Let P=P 1×P 2×...×P M be the direct product of symmetric chain orders P 1, P 2, ..., P M . Let F be a subset of P containing no l+1 elements which are identical in M−1 components and linearly ordered in the Mth one. Then max |F|≤c•M 1/2•l•W(P), where W(P) is the cardinality of the largest level of P, and c is independent of P, M and l. Infinitely many P show that this result is best possible for every M and l apart from the constant factor c.
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Communicated by I. Rival
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Sali, A. A sperner-type theorem. Order 2, 123–127 (1985). https://doi.org/10.1007/BF00334851
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DOI: https://doi.org/10.1007/BF00334851