185 citations · 371 across the 28 of their papers we have counts for
5 papers · 1 filter
Johann Faulhaber and sums of powers
Donald E. Knuth
Early 17th-century mathematical publications of Johann Faulhaber contain some remarkable theorems, such as the fact that the -fold summation of is a polynomial…
Convolution polynomials
Donald E. Knuth
The polynomials that arise as coefficients when a power series is raised to the power include many important special cases, which have surprising properties that are not widely…
Two notes on notation
Donald E. Knuth
The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is th…
Efficient representation of perm groups
Donald E. Knuth
This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about approp…
Stable husbands
Donald E. Knuth, Rajeev Motwani, Boris Pittel
Suppose boys and girls rank each other at random. We show that any particular girl has at least and at most different husbands in the se…