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The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

Q(n), also denoted q(n) (Abramowitz and Stegun 1972, p. 825), gives the number of ways of writing the integer n as a sum of positive integers without regard to order with the ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

The number of partitions of n in which no parts are multiples of k is sometimes denoted b_k(n) (Gordon and Ono 1997). b_k(n) is also the number of partitions of n into at ...

The number of partitions of n with k or fewer addends, or equivalently, into partitions with no element greater than k. This function is denoted q(n,k) or q_k(n). (Note that ...

Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

The party problem, also known as the maximum clique problem, asks to find the minimum number of guests that must be invited so that at least m will know each other or at ...

An apodization function similar to the Bartlett function.

The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...