The Surprising Mathematics of Longest Increasing Subsequences

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Delving into the longest increasing subsequence problem, this book uncovers its profound links to diverse mathematical fields, including random permutations and matrices. It offers a playful exploration of significant theorems such as the Vershik-Kerov-Logan-Shepp limit shape theorem and the Tracy-Widom distribution, making complex concepts approachable for graduate students. By connecting probability and combinatorics, it serves as an engaging introduction to elegant mathematical ideas relevant to mathematicians, computer scientists, and statisticians alike.