swMATH ID: 11565
Software Authors: Aaron Robertson, Dan Saracino, Doron Zeilberger
Description: Refined restricted permutations. Derangements (and more generally the notion of ”fixed points of a permutation”) are concepts related to the cycle-structre, i.e. two-line notation, i.e. permutations qua 1-1 functions from [1,n] to [1,n]. On the other hand, Pattern-avoidance (and Wilf- equivalence) are inherently ”wordy”, i.e. pertain to permutations qua words. Perhaps this is why no one noticed the amazing and easily-stated fact that the number of 132-avoiding derangements equals the number of 321-avoiding derangements, and even more amazingly, that the same is true if you replace ”derangement” by ”with i fixed points”, for ANY \(i\) between \(0\) and \(n\). This astounding fact was first discovered emprically by Aaron Robertson ...
Homepage: http://www.math.rutgers.edu/~zeilberg/programs.html
Dependencies: Maple
Related Software: OEIS; FindStat
Cited in: 27 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Refined restricted permutations. Zbl 1017.05014
Robertson, Aaron; Saracino, Dan; Zeilberger, Doron

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