Timeline for Subgroups of a finite abelian group

5 events

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Mar 3, 2020 at 1:13	history	edited	coudy	CC BY-SA 4.0	corrected missing exponent
Nov 20, 2010 at 7:54	comment	added	Amritanshu Prasad		The number $N_n$ is the Gaussian binomial coefficient $\binom rn_p$. Taking the limit $p\to 1$ gives the usual binomial coefficients. There is an interesting analogous fact for finite abelian groups; if $\lambda$ and $\mu$ are partitions, and $\binom\lambda\mu_p$ is the number of abelian $p$-subgroups of type $\mu$ in an abelian $p$-group of type $\lambda$, then the limit $\p\to 1$ is the answer to a question in multiset combinators: the number of multisets of type $\mu$ in a multiset of type $\lambda$ (see Butler's monograph in my answer above).
Nov 19, 2010 at 11:26	comment	added	Robin Chapman		This kind of numerology generalizes to general finite Abelian $p$-groups via the formalism of Hall polynomials: en.wikipedia.org/wiki/Hall_polynomial .
Nov 19, 2010 at 9:42	history	edited	Neil Strickland	CC BY-SA 2.5	Improved formatting
Nov 19, 2010 at 8:41	history	answered	Neil Strickland	CC BY-SA 2.5