Minimal cogenerators need not be unique |
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Authors: | Barbara L Osofsky |
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Institution: | Department of Mathematics , Rutgers University , New Brunswick, NJ 08903, USA |
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Abstract: | An = An(?) denotes the unique left distributive binary system on {0, 1,…,2n?1) that satisfies a ? 1 = a + 1 mod 2nfor all a ? An, and on(a) = k indicates the period 2kof a ? An (if b,c ? An, then a ? b = a ? c iff b ‵ c mod 2kand if 0 < b < c < 2kthen a < a ? b < a ? c). Amongs others, we prove that ot2(2t?2) ≤ t holds for every integer t ≥ 2, the equality taking place iff t is of the form 22? for an integer s ≥ 0. |
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