On 102-avoiding inversion sequences
Abstract
In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schr\"oder paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled F-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In addition, we study inversion sequences avoiding 102 and another pattern of length 3, providing refined enumerations according to the same statistic.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.