On Bergeron's Positivity Problem for $q$-Binomial Coefficients
نویسندگان
چکیده
منابع مشابه
POSITIVITY PRESERVING TRANSFORMATIONS FOR q-BINOMIAL COEFFICIENTS
Abstract. Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found....
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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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7358