Results 291 to 300 of about 863,417 (323)

BIASES IN INTEGER PARTITIONS

Bulletin of the Australian Mathematical Society, 2021
We show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let $p_{j,k,m} (n)$ be the number of partitions of n such that there are more parts congruent to j modulo ...
Byungchan Kim, Eunmi Kim
semanticscholar   +3 more sources

Integer partitions

Tau Functions and their Applications, 2021
Let L denote the positive octant of the regular d-dimensional cubic lattice. The summands in the d-partition are thus nonincreasing in each of the d lattice directions. We agree to suppress all zero labels.
George E. Andrews
semanticscholar   +1 more source

On integer partitions and continued fraction type algorithms

The Ramanujan journal, 2021
Our goal is to show that the additive-slow-Farey version of the Triangle map (a type of multidimensional continued fraction algorithm) gives us a method for producing a map from the set of integer partitions of a positive number n into itself.
Wael Baalbaki   +4 more
semanticscholar   +1 more source

On Product Partitions of Integers

Canadian Mathematical Bulletin, 1991
AbstractLet p*(n) denote the number of product partitions, that is, the number of ways of expressing a natural number n > 1 as the product of positive integers ≥ 2, the order of the factors in the product being irrelevant, with p*(1) = 1. For any integer if d is an ith power, and = 1, otherwise, and let . Using a suitable generating function for p*(
M. V. Subbarao, V. C. Harris
openaire   +2 more sources

On the distribution of rank and crank statistics for integer partitions

Research in Number Theory, 2018
Let k be a positive integer and m be an integer. Garvan’s k-rank $$N_k(n,m)$$Nk(n,m) is the number of partitions of n into at least $$(k-1)$$(k-1) successive Durfee squares with k-rank equal to m. In this paper we give some asymptotics for $$N_k(n,m)$$Nk(
N. Zhou
semanticscholar   +1 more source

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