What is a combinatorial interpretation?
Igor Pak
TL;DR
This survey explores the concept of combinatorial interpretation within Algebraic Combinatorics, examining its computational complexity, reviewing examples, and discussing open problems and recent developments.
Contribution
It provides a comprehensive definition and analysis of combinatorial interpretation from a computational complexity perspective, highlighting open problems and recent advances.
Findings
Many examples of combinatorial interpretations are reviewed
A workable definition is proposed for the notion
Recent results and open problems are discussed
Abstract
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a workable definition, discuss many open problems, and present recent results on the subject.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic · Advanced Database Systems and Queries