Permutations with few inversions
Abstract
A curious generating function S0(x) for permutations of [n] with exactly n inversions is presented. Moreover, (xC(x))iS0(x) is shown to be the generating function for permutations of [n] with exactly n-i inversions, where C(x) is the generating function for the Catalan numbers.
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.