exception of the ambiguity between the quantum $q$-Krawtchouk and affine $q$-Krawtchouk types.

The second statement is an immediate consequence.

For the third statement, we have to prove that cases $6$ and $7$ of Lemma $\ref{normrules}$ do not apply to $AW$. Assuming the contrary, $AW$ would have the Krawtchouk type. In the corresponding normalized form of Lemma \[awnormals2\] we would have $v\in\{0,1\}$. But then the Krawtchouk parameter array of Lemma \[normlps2\] degenerates, since $\phi_i=0$ or $\psi_i=0$ for all $i=1,2,\ldots,d$. The third statement follows.

The inequalities of the last column of Table \[elltab\] can be checked by inspecting all Askey-Wilson relations in Lemmas \[awnormals\], \[awnormals1\] and \[awnormals2\]. Normalization by affine translations follows from the Lemma \[normrules\] and the previous part here. Normalization by affine scalings is clear.[$\Box$]{}\
Note that the normalization specified by Lemma \[normrules\] follows implications of part 4 of Theorem \[classth\]. By part 3 of Theorem \[classth\], there is a unique affine translation to set two specified Askey-Wilson coefficients to zero. For each type of Leonard pairs, we get two Askey-Wilson coefficients which are certainly nonzero after the normalizing affine translation. These coefficients can be characterized as follows: they are the first nonzero (after the normalizing translation) coefficients in the 