A Continuous Analogue for Young Diagrams

TL;DR

This paper introduces a continuous analogue for Young diagrams, transforming the discrete staircase shape into a continuous form, extending previous research on continuous analogues of combinatorial objects.

Contribution

It develops a novel continuous representation for Young diagrams, providing a new perspective and tools for analyzing combinatorial structures.

Findings

Continuous Young diagrams provide new insights into combinatorial analysis.

The approach generalizes discrete Young diagrams to a continuous setting.

Potential applications in asymptotic combinatorics and representation theory.

Abstract

We build a continuous analogue for Young diagrams, thought of as left-aligned stairs, following the line of research initiated by D\'iaz and Cano on the construction of continuous analogues for combinatorial objects.