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YoungTableaux/Tests/enumerationTests.m2
@@ -27,10 +27,15 @@ TEST ///
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lambda = youngDiagram (n:2);
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assert(#(allStandardYoungTableaux lambda) == binomaial(2*n, n) // (n+1))
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)
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-
+
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-- FACT: Let f(n) = |SYT(n)|. Then the following recurrence relation holds:
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-- f(n) = f(n-1) + (n-1) * f(n-2).
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assert(allStandardYoungTableaux 5 == allStandardYoungTableaux 4 + 4 * allStandardYoungTableaux 3)
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+ -- The number of tableaux generated should agree with the hook-length
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+ -- formualtion used in numberStandardYoungTableaux.
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+ lambda = {4,3,1}
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+ assert(#allStandardYoungTableaux lambda == numberStandardYoungTableaux lambda)
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///
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TEST ///
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