Results 181 to 190 of about 50,648 (222)
Some of the next articles are maybe not open access.
On an Elementary Proof of Some Asymptotic Formulas in the Theory of Partitions
The Annals of Mathematics, 1942Let \(p(n)\) be the number of partitions of the positive integer \(n\) and let \(p_k(n)\) be the number of partitions of \(n\) into exactly \(k\) summands. The author gives an elementary proof that \(\lim_{n \to \infty} n p(n) \exp\{-\pi(2n/3)^{1/2}\}\) exists and is positive, but does not determine its value (known to be \(48^{-1/2}\)).
P. Erdös
openaire +3 more sources
Partitions of Positive Integers: An Elementary Topic of Number Theory
The Mathematics Teacher, 1974The author presents some interesting aspects of number theory and graphing that should be appealing to students.
Gerald E. Lenz
openaire +2 more sources
Congruences modulo powers of 5 for the crank parity function
Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2023In 1988, Andrews and Garvan introduced the partition statistic “crank” in order to give combinatorial interpretation for Ramanujan’s celebrated partition congruence modulo 11. In 2009, Choi, Kang and Lovejoy established congruences modulo powers of 5 for
Dazhao Tang
semanticscholar +1 more source
Congruences modulo powers of 5 for partitions into odd and distinct parts
Quaestiones Mathematicae. Journal of the South African Mathematical SocietyLet Q0(n) denote the number of partitions of n into odd and distinct parts. In 1969, Rødseth proved an infinite family of congruences modulo high powers of 5 for Q0(n) by employing the theory of modular forms.
Dazhao Tang
semanticscholar +1 more source
Elementary proofs of Radu and Sellers’ results for broken 2-diamond partitions
The Ramanujan journal, 2015Bernard L. S. Lin, A. Y. Wang
semanticscholar +2 more sources
Some infinite families of congruences for t-core partition functions
Acta Mathematica Hungarica, 2023S. N. Fathima, U. Pore
semanticscholar +1 more source
Annual Conference for Computer Science Logic, 2023
B. Jacobs, Dario Stein
semanticscholar +1 more source
B. Jacobs, Dario Stein
semanticscholar +1 more source