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-bino
β¦ LIBER β¦
Confluent q-extensions of some classical determinants
β Scribed by Warren P. Johnson
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 148 KB
- Volume
- 411
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
β¦ Synopsis
We evaluate two determinants. The first is a q, h-extension of the classical confluent extension of the Vandermonde determinant. The second is a similar extension of Cauchy's double alternant.
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