# A generalization of Chebyshev polynomials and non rooted posets

## TL;DR

This paper generalizes Chebyshev polynomials and applies the results to determine the M"obius function of a specific poset, providing an affirmative answer to a conjecture by Bj"orner, Sagan, and Vatter.

## Contribution

It introduces a new generalization of Chebyshev polynomials and uses it to analyze the M"obius function of a particular poset structure.

## Key findings

- Derived a formula for the M"obius function of the generalized subword order
- Confirmed the conjecture by Bj"orner, Sagan, and Vatter for the specific poset
- Established a connection between Chebyshev polynomial generalizations and poset combinatorics

## Abstract

In this paper we give a generalization of Chebyshev polynomials and using this we describe the M\"obius function of the generalized subword order from a poset {a1,...as,c |ai<c}, which contains an affirmative answer for the conjecture by Bj\"orner, Sagan, Vatter.[5,10]