3 citations · 5 across the 2 of their papers we have counts for
26 papers · 1 filter
A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture
Shalosh B. Ekhad, Vince Vatter, Doron Zeilberger
We prove, via 30 seconds of Maple computation, that there are 10^n words in the alphabet {3,-2} of length 5n, sum 0, and such that every factor that sums to 0 and that starts with…
Refined Restricted Permutations
Aaron Robertson, Dan Saracino, Doron Zeilberger
Define to be the set of permutations of with exactly fixed points which avoid the pattern . Let be the size of . We in…
Patterns and Fractions
Aaron Robertson, Herb Wilf, Doron Zeilberger
We find, in the form of a continued fraction, the generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to exte…
The Number of Permutations With A Prescribed Number of 132 and 123 Patterns
Shalosh B. Ekhad, Aaron Robertson, Doron Zeilberger
Here we present the reasoning behind, and program to find, the generating functions for the number of permutations in the title. The article duals as the "accompanying" Maple packa…
Proof of a Conjecture of Chan, Robbins, and Yuen
Doron Zeilberger
Using the celebrated Morris Constant Term Identity, we deduce a recent conjecture of Chan, Robbins, and Yuen (math.CO/9810154), that asserts that the volume of a certain …
WZ Theory, Chapter II
Doron Zeilberger
The impact of the computer on present and especially future mathematics is illustrated by means of the iconic example of WZ theory.