A horizontal-strip LLT polynomial is determined by its weighted graph
Abstract
We prove that two horizontal-strip LLT polynomials are equal if the associated weighted graphs defined by the author in a previous paper are isomorphic. This provides a sufficient condition for equality of horizontal-strip LLT polynomials and yields a well-defined LLT polynomial indexed by a weighted graph. We use this to prove some new relations between LLT polynomials and we explore a connection with extended chromatic symmetric functions.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.07984
- arXiv:
- arXiv:2110.07984
- Bibcode:
- 2021arXiv211007984T
- Keywords:
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- Mathematics - Combinatorics;
- Primary 05E05;
- Secondary 05E10;
- 05C15
- E-Print:
- 56 pages