One of the most challenging problems in enumerative combinatorics is to count Wilf classes, where you are given a pattern, or set of patterns, and you are asked to find a “formula”, or at least an efficient algorithm, that inputs a positive integer n and outputs the number of permutations avoiding that pattern. F123, Also to enumerate permutations containing exactly r occurrences of the pattern 123 for r=0,1,2,3, ... but made more efficient for small r, and also shows an approach how to rigorously prove the ”conjectured” expressions for the number of permutations with exactly r occurrences of the pattern 123 for r=1,2,3, [we only did it for r=1, but the approach could be used in general, but is it worth it?]
Keywords for this software
References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Janson, Svante; Nakamura, Brian; Zeilberger, Doron: On the asymptotic statistics of the number of occurrences of multiple permutation patterns (2015)
- Mansour, Toufik; Shattuck, Mark: On avoidance of patterns of the form $\sigma$-$\tau$ by words over a finite alphabet (2015)
- Johansson, Fredrik; Nakamura, Brian: Using functional equations to enumerate 1324-avoiding permutations (2014)
- Nakamura, Brian; Zeilberger, Doron: Using Noonan-Zeilberger functional equations to enumerate (in polynomial time!) generalized Wilf classes (2013)