Singmaster-type results for Stirling numbers and some related diophantine equations

Motivated by the work of David Singmaster, we study the number of times an integer can appear among the Stirling numbers of both kinds. We provide an upper bound for the occurrences of all the positive integers, and present certain questions for further study. Some numerical results and conjectures concerning the related diohantine equations are collected

Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations

We look at Diophantine equations arising from equating classical counting functions such as perfect powers, binomial coefficients and Stirling numbers of the first and second kind. The proofs of the finiteness statements that we give use a variety of methods from modern number theory, such as effective and ineffective tools from Diophantine approximation. As a tool for one part of the statements we establish a theoretical result that gives a more precise description on the structure of the solution set in the theorem, due to Bilu and Tichy, on Diophantine equations with separate variables in the case when infinitely many solutions exist

On equal values of Stirling numbers of the second kind

Tanulmányi rendszerbe betöltv

On equal values of Stirling numbers of the second kind

Tanulmányi rendszerbe betöltv

On equal values of Stirling numbers of the second kind

Tanulmányi rendszerbe betöltv

On equal values of Stirling numbers of the second kind

Tanulmányi rendszerbe betöltv