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Enumerative Combinatorics by Sergey Fomin, Richard P. Stanley

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Image

Figure 7-19. The MacNeille completion of the Bruhat order of Image.

7.105. [3−] If the partitions λ and μ have the same multiset of hook lengths, does it follow that λ and μ are equal or conjugate?
7.106. a. [2] Let v1 = ImagecrImage, the partition with r parts equal to c. Find the expansion of in terms of Schur functions.
b. [3−] Fix r, c, and t. Let π = (πij ...

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