Corrections for

Proofs and Confirmations

Note that a reference to line 7b means the seventh line from the bottom of the page.

pp[75] = 37,745,732,428,153; note that the 9th and 10th digits were transposed
the reference to Figure 1.7 should come in the third line from the bottom, at the end of the sentence that concludes "the bottom level of each shell."
last number should be 7436 instead of 7435
In the formula, (r-k-1)! should be (2r-k-1)!
$A_{n.k}$ should be $A_{n,k}$
This exercise is nonsense. Given a descending plane partition with largest part r, we can always insert above it a row of r (r+1)s. Every descending plane partition fits the definition of being stripped.
y^2 z ++ y z^2 should be y^2 z + y z^2
left side of displayed equation should be: $(1-q)(1-q^2)(1-q^3) \cdots$
left side of displayed equation should be: $\frac{1}{(1-tq)(1-tq^2)(1-tq^3) \cdots}$
delete "is"
the binomial involving y's should have exponenets that are functions of j rather than i: $(y^{3j} - y^{1-3j})$
to clarify, change last two lines to: "equation (2.24) implies that the $a_j$ must be unique."
first product to right of = should be over $1 \leq i < j \leq n$
"negative for $k \equiv \pm 1 \pmod{8}$" should read "negative for $k \equiv \pm 3 \pmod{8}$".
the upper limit on the product should be r rather than l.
change "exactly k parts of size r," to "exactly k parts of size r in the associated shifted plane partition,"
 
in last displayed equation, numerator of last Gaussian polynomial should be "2r - 2 - k" rather than "r - 2 - k".
Show that the conjectured generating function for cyclically symmetric plane partitions that fit inside $\cal{B}(r,r,r)$ can be written as
 
\[ \prod_{i=1}^r \frac{1-q^{3i-1}}{1-q^{3i-2}} \prod_{1 \leq i \leq j \leq r} \frac{1-q^{3(r+i+j-1)}}{1-q^{3(2i+j-1)}}. \]
 
Use {\it Mathematica\/} to show that this conjectured generating function agrees with $\det(I_r+G_r)$ for $ 1 \leq r \leq 5$.
sentence should end "when $\lambda = -1$.
all $n$s should be $k$s.
the last term in the displayed summation should be $(-1)^b h_{a+b+1}$.
the limits on the second product should be $ 1 \leq i < j \leq r$
in the last line of this exercise, the exponent in the numerator of the last fraction should be $a_j+1$
$L_m$ should be $L_r$
The phrase "For the series given in equation (5.10) with real parameters," should read:
 
"For the series $\sum_{k=0}^{\infty} x^k (\alpha)_k (\beta)_k / k! (\gamma)_k$ with $|x| = 1$ and real parameters, "
there should be a factor of $k+1$ in the denominator
there should be a factor of 2 in the numerator
$-c-1-k$ should be $-c-1+k$
misplaced comma, should come after the vector
$I_r + T_j$ should be $I_r + T_r$
$-RA_r^*R{-1}$ should be $-RT_r^*R{-1}$
a factor of $1-q^{r-2/3}$ is missing from the denominator
$\frac{1-q^{|\eta|+ht(\eta)}}{1-q^{ht(\eta)}}$ should be $\frac{1-q^{|\eta|(1+ht(\eta))}}{1-q^{|\eta|ht(\eta)}}$.
(There are two instances of this error.)
linear term should be $29400x$ rather than $24900x$
change "reflection across the $y=x$ plane" to "reflection through the center of the box."
change $(r-i-1,s-j-1,t-k-1)$ to $(r-i+1,s-j+1,t-k+1)$
\[ N_3(r,r,r) = \left( \prod_{i=1}^r \frac{3i-1}{3i-2} \right) \left( \prod_{1 \leq i \leq j \leq r} \frac{r+i+j-1}{2i+j-1} \right). \]
\[ N_4(r,r,r) = \prod_{1 \leq i \leq j \leq r} \frac{i+j+r-1}{i+2j-2}. \]
$N_5(2r+1,2s+1,2t)$
\[ N_8(2r,2r,2r) = \prod_{i=0} ^{r-1}\frac{(3i+1) (6i)! (2i)!}{(4i+1)! (4i)!}. \]
$ n+j)! $ in last denominator should be $ (n+j)! $
insert "non-negative" before "integer entries"
delete "twice"
"perpendicular bisector" should be "angle bisector"
$y_j^{n-1}$ should be $y_j^{n-2}$.
numerator of right-most fraction should be $f(x) - f(xq)$
If we replace $x$ by $xq$ in $D_q^m f(x)$, we get $q^{-m} D_q^m f(xq)$, so right-hand side of each of these equalities also needs a factor of $q^{-3(n-1)(n-2)/2}$
$(q^{3j+3}:q^3)$ should be $(q^{3j+3};q^3)$. Also in that term, a factor of $(t^6 q^{3-3n})^j$ is
missing.

Thanks to the following people who have found errors in Proofs and Confirmations: Robin Chapman, Emeric Deutsch, Neil J. A. Sloane, Paul Terwilliger and his class at UW-Madison, Ronald P. Infante, Eric Kuo, Robert Mills