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Arithmetic of Finite Ordered Sets: Cancellation of Exponents, I

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Abstract

Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying A P ≅ B P, then A ≅ B. We show that this is true in case P is dismantlable to each of its points, or P is connected and each of A and B is dismantlable to each of its covering pairs.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, U.S.A.

    Ralph McKenzie

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  1. Ralph McKenzie
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McKenzie, R. Arithmetic of Finite Ordered Sets: Cancellation of Exponents, I. Order 16, 313–333 (1999). https://doi.org/10.1023/A:1006457114427

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  • DOI: https://doi.org/10.1023/A:1006457114427

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