[seqfan] Re: additions for completeness' sake
Alonso Del Arte
alonso.delarte at gmail.com
Sun Mar 11 18:30:31 CET 2012
> Would this be too much ballast?
> Would anyone ever look them up?
No, it wouldn't be too much ballast, as long as each new entry gives some
idea of the application and mentions symmetric functions. The existing
sequences that don't mention symmetric functions also need to have comments
added on symmetric functions.
Maybe no one would ever look them up directly, but if they're researching
symmetric functions, they would be grateful if those came up in the results.
On Sun, Mar 11, 2012 at 9:42 AM, Neil Sloane <njasloane at gmail.com> wrote:
> Wouter, That's an excellent observation. Please add a comment
> to A124577, and add the others as new sequences!
> Thanks, Neil
> On Sun, Mar 11, 2012 at 9:12 AM, Wouter Meeussen <
> wouter.meeussen at telenet.be
> > wrote:
> > A001700 C(2n+1, n+1): number of ways to put n+1 indistinguishable
> > balls into 2n+1 distinguishable boxes = number of (n+1)-st degree
> > in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.
> > This (Offset 0) sequence thus also counts the monomial symmetric
> > of (degree=number of variables).
> > Now, the monomial symmetric functions are only one of a set of 5, the
> > others are
> > Power Sum Symmetric Polynomials, Complete Homogeneous Symmetric
> > Polynomials, Elementary Symmetric Polynomials and Schur Polynomials:
> > So I looked them up, and it turns out only the Power Sum Symm. poly's
> > a hit in OEIS:
> > 1, 6, 39, 356, 4055, 57786, 983535, 19520264, 441967518
> > A124577: "Define p(alpha) to be the number of H-conjugacy classes where
> > is a Young subgroup of type alpha of the symmetric group S_n. Then a(n) =
> > sum p(alpha) where |alpha| = n and alpha has at most n parts."
> > without ('direct') mention of symmetric functions.
> > no hits for the others:
> > Complete Homogeneous Symmetric Polynomials
> > 1, 7, 55, 631, 8001, 130453, 2323483, 48916087, 1129559068
> > Elementary Symmetric Polynomials
> > 1, 5, 37, 405, 5251, 84893, 1556535, 33175957, 785671039
> > Schur Polynomials
> > 1, 4, 19, 116, 751, 5552, 43219, 366088, 3245311
> > though this one is 'hidden' as main diagonal of triangle A191714.
> > This suggests looking at these symmetric poly's as triangular tables like
> > A191714,
> > with separate entries for their main diagonals and for their row sums.
> > Would this be too much ballast?
> > Would anyone ever look them up?
> > Wouter.
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Alonso del Arte
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