[seqfan] Littlewood-Richardson rule and coefficients in the OEIS

[Wouter Meeussen]

hi all,

only 3 (three) entries. Skinny. See http://oeis.org/A129723

Wiki says:  quote:
In mathematics, the Littlewood–Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood–Richardson rule describes as counting certain skew tableaux. They occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of irreducible representations of general linear groups (or related groups like the special linear and special unitary groups), or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials
end_quote
so, not trivial, I take it.

On the upside:
see:  “An online program, decomposing products of Schur functions using the Littlewood–Richardson rule”

I found a beautiful implementation in Mathematica on the web:
http://sporadic.stanford.edu/bump/match/weight/lwr.m
Copyright 1996 by Daniel Bump (bump at math.stanford.edu)
fast as lightning and correct when checked the-old-fashioned-slow-way (how did they ... gasp! mathematicians!)

Problem:
for each pair of partitions, you get a sequence or set of partions as result.
How do we want to see this in the OEIS?

One approach is to  convert each partition into a prime, and let the resulting set of primes be represented by a unique integer. This needs a *ranking* of partitions over all sizes, as was sometimes (rarely) done for the binary trees.
If you can rank them, then each ‘item’ can be represented by an integer, or uniquely by a prime. Ranking is alas not unique nor agreed upon.

But, seriously, such ‘condensation’ of info is as bad as hiding it! Who would ever ...
Leaves us with the bare ‘count of partitions’ or ‘count of multplicities’. Such a waste!

I’m at a loss, maybe forget it?
Suggestions?

Wouter.