Permutations with a fixed number of occurrences of a pattern: A case generalizing 231
Abstract
We determine a set of permutation patterns q so that the number of permutations with r occurrences of q is asymptotically nr times the number of permutations avoiding q, partially settling a conjecture of Conway and Guttman. We also use these asymptotics to prove nonrationality and nonalgebraicity for certain ordinary generating functions for permutations with r copies of a pattern.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.