Binary Search Tree insertion, the Hypoplactic insertion, and Dual Graded Graphs

TL;DR

This paper explores the application of Fomin's dual graded graph framework to binary search tree insertion and hypoplactic insertion algorithms, revealing new structural insights and generalizations.

Contribution

It extends Fomin's dual graded graph approach to binary search tree and hypoplactic insertions, connecting classical algorithms with dual graded graph theory.

Findings

Fomin's duality framework applies to binary search tree insertion.

The approach generalizes the hypoplactic insertion algorithm.

New structural insights into insertion algorithms are provided.

Abstract

Fomin (1994) introduced a notion of duality between two graded graphs on the same set of vertices. He also introduced a generalization to dual graded graphs of the classical Robinson-Schensted-Knuth algorithm. We show how Fomin's approach applies to the binary search tree insertion algorithm also known as sylvester insertion, and to the hypoplactic insertion algorithm.