Real-rootedness of quartic Jensen polynomials associated with pod ( n )

Key Points

• The aim is to demonstrate that quartic Jensen polynomials associated with partitions have four distinct real roots for all integers.
• Established inequalities for quartic Jensen polynomials using arbitrary-precision error estimates.
• Confirmed positivity of a class of third-order determinants related to these polynomials.
• Generalized results on third-order Toeplitz matrices associated with specific partitions.
• The quartic Jensen polynomial consistently has four distinct real roots for all integers.
• Inequalities derived showed positive bounds for the associated partitions.
• Positivity was confirmed for third-order determinants, corroborating the results for Toeplitz matrices.

Abstract