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Nonisomorphic Ordered Sets with Arbitrarily Many Ranks That Produce Equal Decks
We prove that for any there is a pair of
nonisomorphic ordered sets such that and have equal maximal
and minimal decks, equal neighborhood decks, and there are ranks such that for each the decks obtained by removing the points
of rank are equal. The ranks do not contain
extremal elements and at each of the other ranks there are elements whose
removal will produce isomorphic cards. Moreover, we show that such sets can be
constructed such that only for ranks and , both without extremal
elements, the decks obtained by removing the points of rank are not
equal.Comment: 30 pages, 6 figures, straight LaTe