Research Article

Restricted inversion sequences and Schröder paths

Published in: Quaestiones Mathematicae
Volume 46 , issue 11 , 2023 , pages: 2327–2338

DOI: 10.2989/16073606.2022.2152399

Author(s): David Callan University of Wisconsin-Madison, USA , Toufik Mansour University of Haifa, Israel

Keywords: Primary: 05A15 , Secondary: 05A18 , Inversion sequences , generating trees , pattern-avoiding , Catalan numbers , Schröder paths

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Abstract

In this paper, we find an explicit formula for the number of inversion sequences of length n that avoid each of the pattern sets {021, 010}, {021, 011}, {021, 100, 101}, {021, 000, 101}, and {101, 102, 201}. This is done using either generating trees and generating functions, or combinatorial bijections to restricted Schröder paths.

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