Table 4.

Maximum number of unique permutations considering exchangeability blocks.

Exchangeability	ee	ise
Unrestricted	N!	2N
Unrestricted, repeated rows	$\mathit{N}!{\displaystyle \prod _{\mathit{m}=1}^{\mathit{M}}}\frac{1}{{\mathit{N}}_{\mathit{m}}!}$	2N
Within-block	${\displaystyle \prod _{\mathit{b}=1}^{\mathit{B}}}{\mathit{N}}_{\mathit{b}}!$	2N
Within-block, repeated rows	${\displaystyle \prod _{\mathit{b}=1}^{\mathit{B}}}{\mathit{N}}_{\mathit{b}}!{\displaystyle \prod _{\mathit{m}=1}^{\mathit{M}|\mathit{b}}}\frac{1}{{\mathit{N}}_{\mathit{m}|\mathit{b}}!}$	2N
Whole-block	B!	2B
Whole-block, repeated blocks	$\mathit{B}!{\displaystyle \prod _{\tilde{\mathit{m}}=1}^{\tilde{\mathit{M}}}}\frac{1}{{\mathit{N}}_{\tilde{\mathit{m}}}!}$	2B

B Number of exchangeability blocks (eb).

M Number of distinct rows in X.

M|b Number of distinct rows in X within the b-th block.

$\tilde{\mathit{M}}$ Number of distinct blocks of rows in X.

N Number of observations.

N_b Number of observations in the b-th block.

N_m Number of times each of the M distinct rows occurs in X.

N_m|b Number of times each of the m-th unique row occurs within the b-th block.

${\mathit{N}}_{\tilde{\mathit{m}}}$ Number of times each of the $\tilde{\mathit{M}}$ distinct blocks occurs in X.