On the Least Common Multiple of Q-Binomial Coefficients
نویسندگان
چکیده
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 کاملNair’s and Farhi’s Identities Involving the Least Common Multiple of Binomial Coefficients Are Equivalent
Throughout this note, let N denote the set of nonnegative integers. Define N∗ := N \ {0}. There are lots of known results about the least common multiple of a sequence of positive integers. The most renowned is nothing else than an equivalent of the prime number theory; it says that log lcm(1, 2, ..., n) ∼ n as n approaches infinity (see, for instance [6]), where lcm(1, 2, · · · , n) means the ...
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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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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.
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ژورنال
عنوان ژورنال: Integers
سال: 2010
ISSN: 1867-0652
DOI: 10.1515/integ.2010.029