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 ...

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Shattuck, Mark; Mansour, Toufik: Counting pattern avoiding permutations by number of movable letters (2021)
  2. Fu, Shishuo; Han, Guo-Niu; Lin, Zhicong: (k)-arrangements, statistics, and patterns (2020)
  3. Mansour, Toufik; Shattuck, Mark: Visibility in pattern-restricted permutations (2020)
  4. Rakotomamonjy, Paul M.: Restricted permutations refined by number of crossings and nestings (2020)
  5. Rakotomamonjy, Paul M.; Andriantsoa, Sandrataniaina R.; Randrianarivony, Arthur: Crossings over permutations avoiding some pairs of patterns of length three (2020)
  6. Bukata, Michael; Kulwicki, Ryan; Lewandowski, Nicholas; Pudwell, Lara; Roth, Jacob; Wheeland, Teresa: Distributions of statistics over pattern-avoiding permutations (2019)
  7. Elizalde, Sergi; Troyka, Justin M.: Exact and asymptotic enumeration of cyclic permutations according to descent set (2019)
  8. Hoffman, Christopher; Rizzolo, Douglas; Slivken, Erik: Fixed points of 321-avoiding permutations (2019)
  9. Elizalde, Sergi; Troyka, Justin M.: The number of cycles with a given descent set (2018)
  10. Opler, Michal: Major index distribution over permutation classes (2016)
  11. Eu, Sen-Peng; Fu, Tung-Shan; Pan, Yeh-Jong; Ting, Chien-Tai: Two refined major-balance identities on 321-avoiding involutions (2015)
  12. Trongsiriwat, Wuttisak: Permutation statistics and multiple pattern avoidance (2015)
  13. Barnabei, Marilena; Bonetti, Flavio; Elizalde, Sergi; Silimbani, Matteo: Descent sets on 321-avoiding involutions and hook decompositions of partitions (2014)
  14. Bloom, Jonathan: A refinement of Wilf-equivalence for patterns of length 4 (2014)
  15. Miner, Sam; Pak, Igor: The shape of random pattern-avoiding permutations (2014)
  16. Elizalde, Sergi: Fixed points and excedances in restricted permutations (2012)
  17. Bousquet-Mélou, Mireille: Counting permutations with no long monotone subsequence via generating trees and the kernel method (2011)
  18. Bloom, Jonathan; Saracino, Dan: Another look at bijections for pattern-avoiding permutations (2010)
  19. Humphreys, Katherine: A history and a survey of lattice path enumeration (2010)
  20. Bloom, Jonathan; Saracino, Dan: On bijections for pattern-avoiding permutations (2009)

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