منابع مشابه
On Log-concavity of the Generalized Marcum Q Function
It is shown that, if ν ≥ 1/2 then the generalized Marcum Q function Qν(a, b) is log-concave in b ∈ [0,∞). This proves a conjecture of Sun, Baricz and Zhou (2010). We also point out relevant results in the statistics literature.
متن کاملQ-analogue of a Linear Transformation Preserving Log-concavity
Log-concave and Log-convex sequences arise often in combinatorics, algebra, probability and statistics. There has been a considerable amount of research devoted to this topic in recent years. Let {xi}i≥0 be a sequence of non-negative real numbers. We say that {xi} is Log-concave ( Log-convex resp.) if and only if xi−1xi+1 ≤ xi (xi−1xi+1 ≥ xi resp.) for all i ≥ 1 (relevant results can see [2] an...
متن کاملInductive concavity
Sagan, B.E., Inductive proofs of q-log concavity, Discrete Mathematics 99 (1992) 289-306. We give inductive proofs of q-log concavity for the Gaussian polynomials and the q-Stirling numbers of both kinds. Similar techniques are applied to show that certain sequences of elementary and complete symmetric functions are q-log concave.
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 کاملLog-concavity and q-Log-convexity Conjectures on the Longest Increasing Subsequences of Permutations
Let Pn,k be the number of permutations π on [n] = {1, 2, . . . , n} such that the length of the longest increasing subsequences of π equals k, and let M2n,k be the number of matchings on [2n] with crossing number k. Define Pn(x) = ∑ k Pn,kx k and M2n(x) = ∑ k M2n,kx . We propose some conjectures on the log-concavity and q-log-convexity of the polynomials Pn(x) and M2n(x).
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: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90377-r