A horizontalstrip LLT polynomial is determined by its weighted graph
Abstract
We prove that two horizontalstrip 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 horizontalstrip LLT polynomials and yields a welldefined 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:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07984
 Bibcode:
 2021arXiv211007984T
 Keywords:

 Mathematics  Combinatorics;
 Primary 05E05;
 Secondary 05E10;
 05C15
 EPrint:
 56 pages