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Their numbers can be arranged into a triangle, the triangle of partition numbers, in which the th row gives the partition numbers (), (), …, (): [1] k n
The Special Collections Research Center (SCRC) of the Earl Gregg Swem Library of William & Mary defines the history of the university and promotes and preserves the scholarly pursuits of its faculty, students, alumni, visiting scholars, and friends. The SCRC contributes to the college's scholarly reputation by providing the rare books and ...
The remaining positions in each row are filled by a rule very similar to that for Pascal's triangle: they are the sum of the two values to the left and upper left of the position. Thus, after the initial placement of the number 1 in the top row, it is the last position in its row and is copied to the leftmost position in the next row.
The Library in 2013. Two further stories of public space and stacks are underground. The Albert and Shirley Small Special Collections Library at the University of Virginia is a research library that specializes in American history and literature, history of Virginia and the southeastern United States, the history of the University of Virginia, Thomas Jefferson, and the history and arts of the ...
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The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts. The number q(n) is also equal to the number of partitions of n in which only odd summands are permitted. [20]
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