AARON 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 1017.05014Robertson, Aaron; Saracino, Dan; Zeilberger, Doron 2002 all top 5 Cited by 41 Authors 6 Elizalde, Sergi 4 Mansour, Toufik 4 Saracino, Dan 3 Robertson, Aaron 2 Deutsch, Emeric 2 Pak, Igor 2 Rakotomamonjy, Paul M. 2 Shattuck, Mark A. 2 Troyka, Justin M. 1 Andriantsoa, Sandrataniaina R. 1 Barnabei, Marilena 1 Bonetti, Flavio 1 Bousquet-Mélou, Mireille 1 Brignall, Robert 1 Bukata, Michael 1 Deng, Eva Y. P. 1 Du, Rosena R. X. 1 Eu, Sen-Peng 1 Fu, Shishuo 1 Fu, Tung-Shan 1 Han, Guo-Niu 1 Hoffman, Christopher 1 Huczynska, Sophie 1 Humphreys, Katherine 1 Kulwicki, Ryan 1 Lewandowski, Nicholas 1 Lin, Zhicong 1 Miner, Sam 1 Opler, Michal 1 Pan, Yeh-jong 1 Pudwell, Lara K. 1 Randrianarivony, Arthur 1 Rizzolo, Douglas 1 Roth, Jacob 1 Silimbani, Matteo 1 Slivken, Erik 1 Ting, Chien-Tai 1 Trongsiriwat, Wuttisak 1 Vatter, Vincent Russell 1 Wheeland, Teresa 1 Zeilberger, Doron all top 5 Cited in 16 Serials 6 Journal of Combinatorial Theory. Series A 3 Advances in Applied Mathematics 3 Annals of Combinatorics 2 European Journal of Combinatorics 2 Journal of Integer Sequences 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Journal of Statistical Planning and Inference 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 Journal of Algebraic Combinatorics 1 The Electronic Journal of Combinatorics 1 Journal of Difference Equations and Applications 1 Séminaire Lotharingien de Combinatoire 1 Applicable Analysis and Discrete Mathematics 1 Journal of Combinatorics all top 5 Cited in 7 Fields 26 Combinatorics (05-XX) 3 Computer science (68-XX) 2 Functions of a complex variable (30-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) Citations by Year