On the gaps between q-binomial coefficients
نویسندگان
چکیده
Abstract In this note, we estimate the distance between two q -nomial coefficients ( k n ) q - ? {\left( {_k^n} \right)_q} - {_{k'}^{n'}} , where ( n, k ) ? n ? and ? 2 is an integer.
منابع مشابه
On P,q-binomial Coefficients
In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations. The construction and derivation of these result...
متن کاملSOME 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...
متن کاملBOUNDS ON KRONECKER AND q-BINOMIAL COEFFICIENTS
We present a lower bound on the Kronecker coefficients of the symmetric group via the characters of Sn, which we apply to obtain various explicit estimates. Notably, we extend Sylvester’s unimodality of q-binomial coefficients ( n k ) q as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients.
متن کاملOn the q - log - Concavity of Gaussian Binomial Coefficients 335
We give a combinatorial proof that k l-k-1 l + t q q q q a polynomial in q with nonnegative coefficients for nonnegative integers a, b, k, lwith a>~b and l~>k. In particular, for a=b=n and l=k, this implies the q-log-concavity of the Gaussian binomial coefficients k , which was conjectured q by BUTLER (Proc.
متن کاملSome congruences involving central q-binomial coefficients
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 ∑
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematics
سال: 2021
ISSN: ['2336-1298', '1804-1388']
DOI: https://doi.org/10.2478/cm-2020-0010