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bio website math.uchicago.edu/~vipul
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seen Feb 24 at 4:17
Mathematics Ph.D. student at the University of Chicago

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revised Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
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comment Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
An alternate description that might be easier for explicitly computing the terms of the sequence is that the exponent on any prime $p$ is the greatest integer of $(n - 1)/(p - 1)$. I think one can work this out from your description by choosing as many of the primes as possible to be $p$.
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comment Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
UPDATE: The bound seems to be tight at least up to n = 5. See groupprops.subwiki.org/wiki/… for instance
Jul
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comment Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
Thanks, a very useful response! I appreciate it. I think the sequence description you give is the same as that in OEIS (you have to click through to the description of the other sequence). The relation with the Baker-Campbell-Hausdorff formula (I think) is this: all the denominators in the degree n part of the BCH formula must divide the n^{th} term of the sequence. Some of the denominators may well be smaller, and I'm not sure if the bound is tight (i.e., whether the a_n of the sequence must exactly be the lcm of the denominators).
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revised Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
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comment Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
Thanks. I had originally thought that my construction was like divided power algebras, and it resembles it in some ways, but it didn't seem to fit precisely enough for the setting I was in. I'll check out Barwick's papers.
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asked Introducing division strategically in operads to accommodate formulas like the Baker-Campbell-Hausdorff formula
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accepted Homology groups of divisible and powered (nilpotent) groups
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comment Homology groups of divisible and powered (nilpotent) groups
Thanks! Sorry I missed it in the first read.
Apr
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comment Homology groups of divisible and powered (nilpotent) groups
@Adam: I just took a copy of the Hilton-Mislin-Roitberg book from my library, and reading it, Theorem 4.14 seems to be the closest to what you're saying. However, this theorem seems to explicitly assume that the abelian group that we are using for our coefficients is also local over the appropriate primes, so the result does not seem to apply to coefficients over $\mathbb{Z}$. Am I reading this correctly? Is there a later result that I am missing?