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Ira Gessel's user avatar
Ira Gessel's user avatar
Ira Gessel
  • Member for 14 years, 1 month
  • Last seen this week
  • Brandeis University, Waltham, MA, United States
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Reason for breakdown of a nice binomial identity
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Reason for breakdown of a nice binomial identity
@NooneAtAll If $\sigma\tau$ is the identity then so is $\tau\sigma$ but in general $\tau\sigma\ne\sigma\tau$.
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Number of Laurent monomials of n variables with degree at most d
You can evaluate the sum on $p$ to get $$\sum_q \binom{n}{q}^2\binom{n+d-q}{n},$$ which agrees with Michael Lugo's formula.
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Which power series in $\mathbb{Z}_p[[T]]$ are rational functions?
See mathoverflow.net/questions/249541/… . (This post deals with coefficients in a field, but the criteria will be the same for an integral domain.)
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Coefficients of certain Taylor series
The coefficients of $2g(t)$, as an exponential generating function, are sequence A211393 of the OEIS (oeis.org/A211393) and this formula for $\ln(2g(t))$ can be found there.
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6 7
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9 10
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