Note on some determinants of q-binomial numbers
نویسندگان
چکیده
منابع مشابه
SOME ASYMPTOTIC RESULTS ON q-BINOMIAL COEFFICIENTS
q have been investigated in relation to questions of representation theory concerning the growth of Kronecker coefficients. Further, one of the results of this note, Theorem 2.2, has also been motivated by, and finds a first useful application in the study of the unimodality of partitions with distinct parts that are contained inside certain Ferrers diagrams (see our own paper [10]). For m = ⌊a...
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Motivated by recent works of Sun and Tauraso, we prove some variations on the Green-Krammer identity involving central q-binomial coefficients, such as n−1 ∑ k=0 (−1)kq−(k+1 2 ) [ 2k k ] q ≡ (n 5 ) q−bn 4/5c (mod Φn(q)), where ( n p ) is the Legendre symbol and Φn(q) is the nth cyclotomic polynomial. As consequences, we deduce that 3am−1 ∑
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Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp, will, respectively, denote the ring of p-adic integers, the field, of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp such that |p|p p−νp p 1/p see 1–16 . As well-known definition, the Euler numbers and Genocchi number...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1986
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90108-1