Document Type

Article

Publication Date

3-26-2025

Department

Department of Mathematical Sciences

Abstract

In a paper by the author, Hemmer, Hopkins, and Keith, the concept of a fixed point in a sequence was applied to the sequence of first column hook lengths of a partition. In this paper, we generalize this notion to fixed hook lengths in an arbitrary column of a partition. We establish combinatorial connections between these fixed hooks and colored partitions that have interesting gap and mex-like conditions. Additionally, we obtain several generating functions for hook lengths of a given fixedness by hook length or part size in unrestricted partitions, as well as some classical restrictions such as odd and distinct partitions.

Publisher's Statement

© 2025. Publisher’s version of record: https://doi.org/10.5281/zenodo.15091075

Publication Title

Integers

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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Mathematics Commons

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