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Properly sized brackets in Chapter 7 formula #68

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Properly sized brackets in Chapter 7 formula #68

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2 changes: 1 addition & 1 deletion chapter07.tex
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Expand Up @@ -1039,7 +1039,7 @@ \section{Counting tilings}
for calculating the number of tilings\footnote{Surprisingly,
this formula was discovered in 1961 by two research teams \cite{kas61,tem61}
that worked independently.}:
\[ \prod_{a=1}^{\lceil n/2 \rceil} \prod_{b=1}^{\lceil m/2 \rceil} 4 \cdot (\cos^2 \frac{\pi a}{n + 1} + \cos^2 \frac{\pi b}{m+1})\]
\[ \prod_{a=1}^{\lceil n/2 \rceil} \prod_{b=1}^{\lceil m/2 \rceil} 4 \cdot \left(\cos^2 \frac{\pi a}{n + 1} + \cos^2 \frac{\pi b}{m+1}\right)\]
This formula is very efficient, because it calculates
the number of tilings in $O(nm)$ time,
but since the answer is a product of real numbers,
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