An observation on the determinant of a Sylvester-Kac type matrix

2019/02/20 by da Fonseca, Carlos M., Kılıç, Emrah
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.07626

Abstract

Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.

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• Generalizations of Sylvester's determinantal identity
• Matrices related to the Pascal triangle
• Yet Another Proof of Sylvester's Determinant Identity
• Determinants of matrices related to the Pascal triangle
• A family of determinants associated with a square matrix