Identical Salem Numbers Arising from Two Families of Palindromic Polynomials

AbstractBased on two sequences of characteristic polynomials and subsequent symmetrization andfactorization, we obtain two distinct families of palindromic polynomials. Surprisingly, thesetwo families produce exactly the same Salem numbers. We present three tables: the first twocontain the characteristic polynomials and the resulting palindromic polynomials for each family(20 entries each), and the third lists the common Salem numbers. All polynomials satisfy thedefining criteria of Salem polynomials, verified numerically with SageMath. The computationsalso benefited from the conversational assistance of DeepSeek.