Catalan numbers and a conjecture on the maximum composition length of a Kac module

Q: What type of study is this?

This is a Quantitative Study study.

Ian M. Musson

doi:10.48550/arxiv.2509.10868

September 13, 2025Open Access

Catalan numbers and a conjecture on the maximum composition length of a Kac module

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Key Points

The maximum number of composition factors of a Kac module is determined, showcasing a direct result from the conjecture.
Our findings validate the conjecture, providing a critical link between Kac modules and Catalan numbers.
Using elementary principles of continuous functions, we establish the proof framework for the conjecture.
The implications of this research could enhance understanding of Lie superalgebras and their modules.

Implication

We prove a conjecture about composition factors in Kac modules for the Lie superalgebra, implying new insights into algebraic structures.

Abstract

We prove a conjecture on the maximum number of composition factors of a Kac module for the Lie superalgebra =(r|r). The proof uses some elementary facts about continuous functions.

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Cite This Study

Ian M. Musson (2025) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0928e https://doi.org/10.48550/arxiv.2509.10868

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Catalan numbers and a conjecture on the maximum composition length of a Kac module

Key Points

Implication

Abstract

Discussion

Cite This Study

Catalan numbers and a conjecture on the maximum composition length of a Kac module

Key Points

Implication

Abstract

Discussion

Cite This Study

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