Note on some determinants of q-binomial numbers

✍ Scribed by K.V Menon

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 160 KB
• Volume: 61
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(86)90108-1

✦ Synopsis

Let a(x)= E~ (-1)"a,,x n and b(x)= ~ b,,x" be two elements in the ring of formal power series such that a(x). b(x)= 1. If ()-l,)-z,...,)tp) and (~I, Z~,..., 2q) are conjugate partitions, we prove that det(axi_i+j)= det(bx;_i+j). Using this result we evaluate a determinant whose elements are q-binomial coefficients.