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Results tagged with algebraic-combinatorics
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user 16002
4
votes
What are the most important open problems in algebraic combinatorics?
One basic problem is to give a combinatorial formula (or "Littlewood-Richardson rule") for the Schubert structure constants. There is a basis $\{ X_w \}$ of the polynomial ring $\mathbb{Z}[x_1,x_2,\d …
21
votes
1
answer
2k
views
Why are the power symmetric functions sums of hook Schur functions only?
One interesting fact in symmetric function theory is that the power symmetric function $p_n$ can be written as an alternating sum of hook Schur functions $s_{\lambda}$:
$$
p_n = \sum_{k+\ell = n} (-1) …
- 1,780