-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 equation involving special prime numbers
Let be the floor function. In this paper, we prove by asymptotic formula that when , then every sufficiently large positive integer can be represented in the form where , , , , are primes such that .
A diophantine inequality involving prime powers