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README.md
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@@ -19,9 +19,10 @@ their product can be written as a linear combination of Schubert polynomials
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Where the sum runs over permutations in \\(S_{n+m}\\). The question is whether the
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\\(c^{\gamma}_{\alpha \beta}\\) (the *structure constants*) have a combinatorial interpretation.
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To give an example of what we mean by combinatorial interpretation, when Schur polynomials
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(which
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the coefficients in the resulting product are equal to the number of semistandard tableaux
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satisfying certain properties
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## Example
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\\(\mathfrak{S}_{\alpha}\mathfrak{S}_{\beta} = x_1^2 + x_1x_2\\). As
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\\(\mathfrak{S}_{2 3 1} = x_1x_2\\) and \\(\mathfrak{S}_{3 1 2} = x_1^2\\) we can write
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\\(\mathfrak{S}_{\alpha}\mathfrak{S}_{\beta} = \mathfrak{S}_{2 3 1} + \mathfrak{S}_{3 1 2}\\).
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It follows that \\(
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and otherwise \\(c_{\alpha,\beta}^{\gamma} = 0\\).
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## Dataset
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Where the sum runs over permutations in \\(S_{n+m}\\). The question is whether the
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\\(c^{\gamma}_{\alpha \beta}\\) (the *structure constants*) have a combinatorial interpretation.
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To give an example of what we mean by combinatorial interpretation, when Schur polynomials
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(which are a subset of Schubert polynomials) are multiplied together,
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the coefficients in the resulting product are equal to the number of semistandard tableaux
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satisfying certain properties (this is known as the
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[Littlewood-Richardson rule](https://en.wikipedia.org/wiki/Littlewood%E2%80%93Richardson_rule)).
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## Example
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\\(\mathfrak{S}_{\alpha}\mathfrak{S}_{\beta} = x_1^2 + x_1x_2\\). As
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\\(\mathfrak{S}_{2 3 1} = x_1x_2\\) and \\(\mathfrak{S}_{3 1 2} = x_1^2\\) we can write
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\\(\mathfrak{S}_{\alpha}\mathfrak{S}_{\beta} = \mathfrak{S}_{2 3 1} + \mathfrak{S}_{3 1 2}\\).
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It follows that for these \\(\alpha\\) and \\(\beta\\), \\(c_{\alpha,\beta}^{\gamma} = 1\\)
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if \\(\gamma = 2 3 1\\) or \\(\gamma = 3 1 2\\)
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and otherwise \\(c_{\alpha,\beta}^{\gamma} = 0\\).
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## Dataset
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