Enumeration schemes and, more importantly, their automatic generation. With all due respect to Wilf classes and enumeration, and even to combinatorics, the main point of this article is not to enhance our understanding of Wilf classes, but to illustrate how much (if not all) of mathematical research will be conducted in a few years. It goes as follows. Suppose a (as of now, human) mathematicians has a brilliant idea. Teach that idea to a computer and let the computer `do research’ using that idea.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Bean, Christian; Gudmundsson, Bjarki; Ulfarsson, Henning: Automatic discovery of structural rules of permutation classes (2019)
  2. Mansour, Toufik; Shattuck, Mark; Wagner, Stephan: Counting subwords in flattened partitions of sets (2015)
  3. Baxter, Andrew M.: Refining enumeration schemes to count according to permutation statistics (2014)
  4. Daly, Daniel; Pudwell, Lara: Pattern avoidance in the rook monoid (2014)
  5. Godbole, Anant; Goyt, Adam; Herdan, Jennifer; Pudwell, Lara: Pattern avoidance in ordered set partitions (2014)
  6. Mansour, Toufik; Shattuck, Mark: Some enumerative results related to ascent sequences (2014)
  7. Aleksandrowicz, Gadi; Asinowski, Andrei; Barequet, Gill: Permutations with forbidden patterns and polyominoes on a twisted cylinder of width 3 (2013)
  8. Baxter, Andrew M.; Pudwell, Lara K.: Enumeration schemes for vincular patterns (2012)
  9. Mansour, Toufik; Schork, Matthias; Shattuck, Mark: Catalan numbers and pattern restricted set partitions (2012)
  10. Mansour, Toufik; Shattuck, Mark: Pattern-avoiding set partitions and Catalan numbers (2011)
  11. Firro, Ghassan; Mansour, Toufik: Restricted (k)-ary words and functional equations (2009)
  12. Albert, M. H.; Elder, M.; Rechnitzer, A.; Westcott, P.; Zabrocki, M.: On the Stanley--Wilf limit of 4231-avoiding permutations and a conjecture of Arratia (2006)
  13. Vatter, Vincent: Finitely labeled generating trees and restricted permutations (2006)
  14. Kremer, Darla; Shiu, Wai Chee: Finite transition matrices for permutations avoiding pairs of length four patterns (2003)
  15. Zeilberger, Doron: Enumeration schemes and, more importantly, their automatic generation (1998)