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A330490
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Total number of permutation arrays of side length n and dimension k as defined by Eriksson and Linusson (2000a); square array T(n,k), read by ascending antidiagonals, for n, k >= 1.
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1
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1, 1, 1, 1, 2, 1, 1, 6, 5, 1, 1, 24, 70, 15, 1, 1, 120, 2167, 1574, 52, 1, 1, 720, 130708, 968162, 69874, 203, 1, 1, 5040, 14231289
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OFFSET
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1,5
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COMMENTS
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The poset P_{3 x 3} of (3 x 3 x 3)-permutation arrays is shown in Figure 1 on p. 209 of Eriksson and Linuson (2000a). We have |P_{3 x 3}| = T(3,3) = 70. The numbers in this rectangular array are copied from Table 1 (p. 210) of the same paper.
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LINKS
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FORMULA
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T(n,k) >= (n!)^(k-1) = A225816(k-1, n).
T(n,k=3) <= n!*2^(binomial(n+1,2) - 1).
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EXAMPLE
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Array T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows, where * indicates a missing number:
1, 1, 1, 1, 1, ...
1, 2, 5, 15, 52, ...
1, 6, 70, 1574, 69874, ...
1, 24, 2167, 968162, *, ...
1, 120, 130708, *, *, ...
1, 720, 14231289, *, *, ...
1, 5040, 2664334184, *, *, ...
1, 40320, 831478035698, *, *, ...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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