Recipe for d-Complete Hook Lengths

Let P be a d-complete poset.

Assign a positive integer h_y to each element y of P as follows:

(initialize) If y is not in the neck of a d(k) interval for some k >= 3, then

h_y := the number of elements in P which are < = y.

(recurse) If y is in the neck of a d(k) interval D for some k >= 3, then

h_y := h_L + h_R - h_S,
where L and R are the "elbow" elements of D and S is the "sister" element to y in the tail of D.

A more precise version of our home page Theorem 2 is:

Theorem 2. Let P be a d-complete poset. Then the product of (1-x^h_y)^-1 over the elements y of P
is an expression for Stanley's P-partition generating function for P.

Move on to Generalization of FRT Hook Formula for Standard Young Tableaux

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