Horizontal and vertical log-concavity
نویسندگان
چکیده
Abstract Horizontal and vertical generating functions recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal log-concavity of sequences assigned to polynomials which show up in combinatorics, number theory physics. This includes Laguerre polynomials, Pochhammer D’Arcais Nekrasov–Okounkov polynomials.
منابع مشابه
Matroids and log-concavity
We show that f -vectors of matroid complexes of realizable matroids are strictly log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realizable matroid form a log-concave sequence. We also prove a statement on log-concavity of h-vectors which strengthens a result by Brown and ...
متن کاملBell Numbers, Log-concavity, and Log-convexity
Let fb k (n)g 1 n=0 be the Bell numbers of order k. It is proved that the sequence fb k (n)=n!g 1 n=0 is log-concave and the sequence fb k (n)g 1 n=0 is log-convex, or equivalently, the following inequalities hold for all n 0, 1 b k (n + 2)b k (n) b k (n + 1) 2 n + 2 n + 1 : Let f(n)g 1 n=0 be a sequence of positive numbers with (0) = 1. We show that if f(n)g 1 n=0 is log-convex, then (n)(m) (n...
متن کاملLog-Concavity and Symplectic Flows
We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.
متن کاملLog-concavity and LC-positivity
A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑n k=r a(n, k)q k is q-log-concave. It is double LC-positive if both triangles {a(n, k)} and {a(n, n − k)} are LC-positive. We show that if {a(n, k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by zn = ∑n k=0 a(n, k)xk, and if {a(n, ...
متن کاملNegative correlation and log-concavity
OF THE DISSERTATION Negative correlation and log-concavity by Michael Neiman Dissertation Director: Jeff Kahn This thesis is concerned with negative correlation and log-concavity properties and relations between them, with much of our motivation provided by [40], [46], and [12]. Our main results include a proof that “almost exchangeable” measures satisfy the “FederMihail” property; counterexamp...
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: Research in number theory
سال: 2021
ISSN: ['2363-9555', '2522-0160']
DOI: https://doi.org/10.1007/s40993-021-00245-1