History of Schur polynomials $s_\lambda$

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2026-08-27 11:06 bmatschke the Schur polynomials, by Jacobi-Trudi current reviewed
2026-08-27 11:06 bmatschke with claude-opus-5 proposed from schur.yaml

What changed between 2026-08-27 11:06 and 2026-08-27 11:06

from line 55 (155 lines, 152 more than before) @@ -55,3 +55,155 @@
       \ alphabet=[str(g) for g in R.gens()]))\n\nschur(4, [3, 2])                \       \ # a partition of 5, past this table"-Numbers: []+Numbers:+- params:+    n: '1'+    lambda: '1'+  number: x1+- params:+    n: '1'+    lambda: '2'+  number: x1^2+- params:+    n: '1'+    lambda: '3'+  number: x1^3+- params:+    n: '1'+    lambda: '4'+  number: x1^4+- params:+    n: '2'+    lambda: '1'+  number: x1 + x2+- params:+    n: '2'+    lambda: '2'+  number: x1^2 + x1*x2 + x2^2+- params:+    n: '2'+    lambda: 1,1+  number: x1*x2+- params:+    n: '2'+    lambda: '3'+  number: x1^3 + x1^2*x2 + x1*x2^2 + x2^3+- params:+    n: '2'+    lambda: 2,1+  number: x1^2*x2 + x1*x2^2+- params:+    n: '2'+    lambda: '4'+  number: x1^4 + x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x2^4+- params:+    n: '2'+    lambda: 3,1+  number: x1^3*x2 + x1^2*x2^2 + x1*x2^3+- params:+    n: '2'+    lambda: 2,2+  number: x1^2*x2^2+- params:+    n: '3'+    lambda: '1'+  number: x1 + x2 + x3+- params:+    n: '3'+    lambda: '2'+  number: x1^2 + x1*x2 + x2^2 + x1*x3 + x2*x3 + x3^2+- params:+    n: '3'+    lambda: 1,1+  number: x1*x2 + x1*x3 + x2*x3+- params:+    n: '3'+    lambda: '3'+  number: x1^3 + x1^2*x2 + x1*x2^2 + x2^3 + x1^2*x3 + x1*x2*x3 + x2^2*x3 + x1*x3^2+    + x2*x3^2 + x3^3+- params:+    n: '3'+    lambda: 2,1+  number: x1^2*x2 + x1*x2^2 + x1^2*x3 + 2*x1*x2*x3 + x2^2*x3 + x1*x3^2 + x2*x3^2+- params:+    n: '3'+    lambda: 1,1,1+  number: x1*x2*x3+- params:+    n: '3'+    lambda: '4'+  number: x1^4 + x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x2^4 + x1^3*x3 + x1^2*x2*x3 + x1*x2^2*x3+    + x2^3*x3 + x1^2*x3^2 + x1*x2*x3^2 + x2^2*x3^2 + x1*x3^3 + x2*x3^3 + x3^4+- params:+    n: '3'+    lambda: 3,1+  number: x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x1^3*x3 + 2*x1^2*x2*x3 + 2*x1*x2^2*x3 ++    x2^3*x3 + x1^2*x3^2 + 2*x1*x2*x3^2 + x2^2*x3^2 + x1*x3^3 + x2*x3^3+- params:+    n: '3'+    lambda: 2,2+  number: x1^2*x2^2 + x1^2*x2*x3 + x1*x2^2*x3 + x1^2*x3^2 + x1*x2*x3^2 + x2^2*x3^2+- params:+    n: '3'+    lambda: 2,1,1+  number: x1^2*x2*x3 + x1*x2^2*x3 + x1*x2*x3^2+- params:+    n: '4'+    lambda: '1'+  number: x1 + x2 + x3 + x4+- params:+    n: '4'+    lambda: '2'+  number: x1^2 + x1*x2 + x2^2 + x1*x3 + x2*x3 + x3^2 + x1*x4 + x2*x4 + x3*x4 + x4^2+- params:+    n: '4'+    lambda: 1,1+  number: x1*x2 + x1*x3 + x2*x3 + x1*x4 + x2*x4 + x3*x4+- params:+    n: '4'+    lambda: '3'+  number: x1^3 + x1^2*x2 + x1*x2^2 + x2^3 + x1^2*x3 + x1*x2*x3 + x2^2*x3 + x1*x3^2+    + x2*x3^2 + x3^3 + x1^2*x4 + x1*x2*x4 + x2^2*x4 + x1*x3*x4 + x2*x3*x4 + x3^2*x4+    + x1*x4^2 + x2*x4^2 + x3*x4^2 + x4^3+- params:+    n: '4'+    lambda: 2,1+  number: x1^2*x2 + x1*x2^2 + x1^2*x3 + 2*x1*x2*x3 + x2^2*x3 + x1*x3^2 + x2*x3^2 ++    x1^2*x4 + 2*x1*x2*x4 + x2^2*x4 + 2*x1*x3*x4 + 2*x2*x3*x4 + x3^2*x4 + x1*x4^2 ++    x2*x4^2 + x3*x4^2+- params:+    n: '4'+    lambda: 1,1,1+  number: x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4+- params:+    n: '4'+    lambda: '4'+  number: x1^4 + x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x2^4 + x1^3*x3 + x1^2*x2*x3 + x1*x2^2*x3+    + x2^3*x3 + x1^2*x3^2 + x1*x2*x3^2 + x2^2*x3^2 + x1*x3^3 + x2*x3^3 + x3^4 + x1^3*x4+    + x1^2*x2*x4 + x1*x2^2*x4 + x2^3*x4 + x1^2*x3*x4 + x1*x2*x3*x4 + x2^2*x3*x4 ++    x1*x3^2*x4 + x2*x3^2*x4 + x3^3*x4 + x1^2*x4^2 + x1*x2*x4^2 + x2^2*x4^2 + x1*x3*x4^2+    + x2*x3*x4^2 + x3^2*x4^2 + x1*x4^3 + x2*x4^3 + x3*x4^3 + x4^4+- params:+    n: '4'+    lambda: 3,1+  number: x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x1^3*x3 + 2*x1^2*x2*x3 + 2*x1*x2^2*x3 ++    x2^3*x3 + x1^2*x3^2 + 2*x1*x2*x3^2 + x2^2*x3^2 + x1*x3^3 + x2*x3^3 + x1^3*x4 ++    2*x1^2*x2*x4 + 2*x1*x2^2*x4 + x2^3*x4 + 2*x1^2*x3*x4 + 3*x1*x2*x3*x4 + 2*x2^2*x3*x4+    + 2*x1*x3^2*x4 + 2*x2*x3^2*x4 + x3^3*x4 + x1^2*x4^2 + 2*x1*x2*x4^2 + x2^2*x4^2+    + 2*x1*x3*x4^2 + 2*x2*x3*x4^2 + x3^2*x4^2 + x1*x4^3 + x2*x4^3 + x3*x4^3+- params:+    n: '4'+    lambda: 2,2+  number: x1^2*x2^2 + x1^2*x2*x3 + x1*x2^2*x3 + x1^2*x3^2 + x1*x2*x3^2 + x2^2*x3^2+    + x1^2*x2*x4 + x1*x2^2*x4 + x1^2*x3*x4 + 2*x1*x2*x3*x4 + x2^2*x3*x4 + x1*x3^2*x4+    + x2*x3^2*x4 + x1^2*x4^2 + x1*x2*x4^2 + x2^2*x4^2 + x1*x3*x4^2 + x2*x3*x4^2 ++    x3^2*x4^2+- params:+    n: '4'+    lambda: 2,1,1+  number: x1^2*x2*x3 + x1*x2^2*x3 + x1*x2*x3^2 + x1^2*x2*x4 + x1*x2^2*x4 + x1^2*x3*x4+    + 3*x1*x2*x3*x4 + x2^2*x3*x4 + x1*x3^2*x4 + x2*x3^2*x4 + x1*x2*x4^2 + x1*x3*x4^2+    + x2*x3*x4^2+- params:+    n: '4'+    lambda: 1,1,1,1+  number: x1*x2*x3*x4 

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