Enumeration of Hollow Equal Length Shifted Standard Young Tableaux Based on Occupy Model
By using the correspondence between nested order statistics and standard Young tableaux,the enumeration of the standard Young tableaux is transformed into a multiple integration problem on[0,1]uniformly distributed nested order statistics on intervals.Based on the one-to-one correspon-dence between the hollow equal length shifted standard Young tableaux and the nested simplex,an oc-cupancy model is established.Combined with the Python algorithm,the model is analyzed and solved to obtain the counting formula for the hollow equal length shifted standard Young tableaux with 4 cells in each row,resulting in a 2n-1 Fibonacci sequence.Based on this occupancy model,a more gen-eral counting formula for the hollow equal length shifted standard Young tableaux are derived.
Standard Young tableauxHollow equal length shifted shapesOccupancy model2n-1 Fi-bonacci sequencePython algorithm
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