-enumeration of self-complementary plane partitions.
1974 conjecture of Andrews on partitions.
4-core partitions and class numbers
A Best Covering Problem.
A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin.
A binomial coefficient identity associated with Beukers' conjecture on Apéry numbers.
A Bound for Prime Solutions of Some Ternary Equations.
A certain generalization of a result of Erdös and Surányi
A class of finite -series - II
A class of finite -series. - III
A closer look at lattice points in rational simplices.
A closer look at some new identities.
A combinatorial approach to partitions with parts in the gaps
Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then .
A combinatorial proof of Andrews' smallest parts partition function.
A combinatorial proof of the sum of -cubes.
A complete Vinogradov 3-primes theorem under the Riemann hypothesis.
A conditional result on Goldbach numbers in short intervals
A connection between ordinary partitions and tilings with dominoes and squares.
A diophantine inequality involving prime powers
A Diophantine inequality with four squares and one th power of primes
Let be an odd integer and be any given real number. We prove that if , , , , are nonzero real numbers, not all of the same sign, and is irrational, then for any real number with , the inequality has infinitely many solutions in prime variables , where for and for odd integer with . This improves a recent result in W. Ge, T. Wang (2018).