The bias of three pseudo-random shuffles.
The bias of three pseudo-random shuffles. (Short Communication).
The Borwein conjecture and partitions with prescribed hook differences.
The finite Heine transformation and conjugate Durfee squares.
The generating function of ternary trees and continued fractions.
The integer sequence A002620 and upper antagonistic functions.
The lattice of threshold graphs.
The major counting of nonintersecting lattice paths and generating functions for tableaux. (Summary).
The moments of partitions, I
The monoid of ordered partitions of a natural number.
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
The polynomial part of a restricted partition function related to the Frobenius problem.
The -binomial theorem and two symmetric -identities.
The size of the largest part of random plane partitions of large integers.
The spt-crank for overpartitions
Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions , , , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...
The weighted hook length formula. III: Shifted tableaux.
There are no Golay complementary sequences of length 2.9t.
Three aspects of partitions.
Three restricted product-sum partition functions
Topological degree and Sperner's lemma