Bob Proctor sent me an email explaining that the poset $P$ corresponding to the (unshifted, straight) shape $\lambda = (p+(r-1)b, p+(r-2)b, ..., p+b, p)$ has a product formula for its order polynomial, which can be seen via manipulations on the appropriate determinant. Note that this class includes both rectangles ($b=0$), as well as staircases ($p=1$, $b=1$). A reference for this result (with attribution to Proctor) is Stanley's EC2 Exercise 7.101.

Bob Proctor sent me an email explaining that the poset $P$ corresponding to the (unshifted, straight) shape $\lambda = (p+(r-1)b, p+(r-2)b, ..., p+b, p)$ has a product formula for its order polynomial, which can be seen via manipulations on the appropriate determinant. Note that this class includes both rectangles ($b=0$), as well as staircases ($p=1$, $b=1$). A reference for this result (with attribution to Proctor) is Stanley's EC2 Exercise 7.101. It is also mentioned in Proctor's paper "Odd symplectic groups."

Bob Proctor sent me an email explaining that the poset $P$ corresponding to the (unshifted, straight) shape $\lambda = (p+(r-1)b, p+(r-2)b, ..., p+b, p)$ has a product formula for its order polynomial, which can be seen via manipulations on the appropriate determinant. Note that this class includes both rectangles ($b=0$), as well as staircases ($p=1$, $b=1$).

Bob Proctor sent me an email explaining that the poset $P$ corresponding to the (unshifted, straight) shape $\lambda = (p+(r-1)b, p+(r-2)b, ..., p+b, p)$ has a product formula for its order polynomial, which can be seen via manipulations on the appropriate determinant. Note that this class includes both rectangles ($b=0$), as well as staircases ($p=1$, $b=1$). A reference for this result (with attribution to Proctor) is Stanley's EC2 Exercise 7.101.