New determinant expressions of Bernoulli, Euler & Tribonacci polynomials

AIMS Mathematics 2026 Open access

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Authors: Takao Komatsu, Fatih Yilmaz
DOI: 10.3934/math.2026044
Cited by: 1
References: 24

Abstract

In 1875, Glaisher systematically found several interesting determinant expressions of numbers, including Bernoulli, Cauchy, and Euler numbers. In this paper, we identify several determinants that express Euler polynomials. Goy and Shattuck presented several determinantal expressions of some families of Toeplitz–Hessenberg matrices with Tribonacci number entries. However, a determinant expression of Tribonacci numbers has not been studied much. By using a similar form of determinants to Euler's, we also give some determinant representations of generalized Tribonacci numbers.

Fields of Study & Subjects

Advanced Mathematical Theories and Applications Advanced Combinatorial Mathematics Advanced Mathematical Identities

Publication details

Journal / source
AIMS Mathematics
Publisher
American Institute of Mathematical Sciences (AIMS)
Volume
11
Issue
1
Pages
1021–1035
Publication date
1 January 2026