[seqfan] Schur Polynomials

wouter meeussen wouter.meeussen at pandora.be
Tue Dec 14 21:32:29 CET 2010


for all partitions upto n=20 (=2713 partitions).
tabulated extensively for v=1 .. 8 variables, but with a (still conjectured)
trick to calculate them for any v in O(k) with k the count of parts in the
Could be useful, but it certainly was fun to study the available internet
presentations and calculate'm.
Presented in Excel to make use of the elegant tabulation, not as calculator.

The Mathematica code (old Mma 4.0.1) is included.
Where relevant, the internet sources are shown.

Problem \ Question.

I stumbled upon a set of coefficients (that I called "ksi", cfr column Z),
that (seem to) allow to calculate the Schur polynomials simply on the basis
of the multinomial of the content (count of different entries) of the
partition itself.
So, that 'ksi' is the multiplier needed to go from 'content of the
partition' to
'content of the SSYT's ' with that shape. Mysterious.

The coefficients 'ksi' fit with the two other calculation methods:
1.    by determinants
2.    by generation of SSYT
3.    by the ksi-trickery

Does that 'ksi' have proper name?


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