Quantized dual graded graphs

TL;DR

This paper introduces the concept of quantized dual graded graphs, exploring their properties and providing examples based on combinatorial structures like Fibonacci posets, permutations, Young tableaux, and binary trees.

Contribution

It defines quantized dual graded graphs with a specific operator relation and constructs multiple examples from well-known combinatorial objects.

Findings

Established the relation DU - qUD = rI for quantized dual graded graphs

Constructed examples from Fibonacci poset, permutations, Young tableaux, and binary trees

Provided a framework for studying quantized dual graded graphs in combinatorics

Abstract

We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU - qUD = rI. We construct examples based upon: the Fibonacci poset, permutations, standard Young tableau, and plane binary trees.