26 citations · 26 across the 5 of their papers we have counts for
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On Generalized Van der Waerden Triples
Bruce Landman, Aaron Robertson
Van der Waerden's classical theorem on arithmetic progressions states that for any positive integers k and r, there exists a least positive integer, w(k,r), such that any r-colorin…
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…
Difference Ramsey Numbers and Issai Numbers
Aaron Robertson
We present a recursive algorithm for finding good lower bounds for the classical Ramsey numbers. Using notions from this algorithm we then give some results for generalized Schur n…
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…
Permutations Containing and Avoiding 123 and 132 Patterns
Aaron Robertson
We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern equals (n-2)2^(n-3). We then give a bijection onto the set of permutations which…