On some 2-adic properties of a recurrence involving stirling numbers |
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Authors: | T Lengyel |
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Institution: | 1.Mathematics Department,Occidental College,Los Angeles,USA |
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Abstract: | We analyze some 2-adic properties of the sequence defined by the recurrence Z(1) = 1; Z(n) = Σ k=1 n−1 S(n, k)Z(k), n ≥ 2, which counts the number of ultradissimilarity relations, i.e., ultrametrics on an n-set. We prove the 2-adic growth property ν 2(Z(n)) ≥ ⌈log2 n⌉ −1 and present conjectures on the exact values. |
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