# integer partition

## integer partition

[′int·ə·jər pär′tish·ən]
(mathematics)
For a positive integer n, a nonincreasing sequence of positive integers whose sum equals n.
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and NEGPAR([pi]) to be the integer partition with part [absolute value of [[pi].
r]) is the multi-degree of w then {w} is just a [lambda]-tabloid, where [lambda] may be, without loss of generality, assumed an integer partition of n.
INTEGER PARTITION NUMBER 1 1 2 2 3 3 4 5 5 7 6 11 7 15 8 22 9 30 10 42 11 56 12 77 13 101 14 135 15 176 16 231 17 297 18 385 19 490 20 627 21 792 22 1,002 PARTITIONS OF 4 RANK GROUP NUMBER 4 4 - 1 = 3 3 3 + 1 3 - 2 = 1 1 3 + 2 2 - 2 = 0 0 2 + 1 + 1 2 - 3 = -1 4 1 + 1 + 1 + 1 1 - 4 = -3 2
While generating function proofs such as those supplied by MacMahon and Andrews are of great value, bijective proofs of such integer partition identities are also quite beneficial.
l] there is an integer partition [lambda](w) = ([[lambda].
Denote by [LAMBDA]([pi]) the unique integer partition defined by (#[[pi].
The proof of Theorem 1 requires working knowledge of the theory of integer partition, especially its representation as Young diagrams, the Hasse diagram of the Young lattice, and the RSK-algorithm for filling positive integers to obtain the beginning of some standard Young tableau.
n an integer partition of n with l([lambda]) = p parts sorted in decreasing order.
alpha]] can be interpreted, as we have seen already in Section 3, as an integer partition.
An integer partition [lambda] of a non-negative integer n is a multiset of positive integers whose sum is n.
It is common to associate to a set-partition the integer partition formed by the non-increasing sequence of the part sizes.
Notice that the quantity [absolute value of [mu]] - l([mu]) is not changed if one adds or removes parts of size 1 to the integer partition In the following, we shall rather work with renormalized character values [[summation].

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