Results 1 to 10 of about 271 (36)

Recursive determination of the enumerator for sums of three squares

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 8, Page 529-532, 2000., 2000
For each nonnegative integer n, r3(n) denotes the number of representations of n by sums of three squares. Here presented is a two‐step recursive scheme for computing r3(n), n ≥ 0.
John A. Ewell
wiley   +1 more source

The hyperbolicity constant of infinite circulant graphs

Open Mathematics, 2017
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.
Rodríguez José M., Sigarreta José M.
doaj   +1 more source

Compositions inside a rectangle and unimodality [PDF]

, 2007
Let c^{k,l}(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k-by-l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c^{k,l}(0),
Sagan, Bruce E.
core   +4 more sources

A generalized formula of Hardy

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 369-378, 1994., 1994
We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi‐crystal structure and self‐similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood′s High Indices ...
Geoffrey B. Campbell
wiley   +1 more source

The log-convexity of the poly-Cauchy numbers

, 2016
In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In
Komatsu, Takao, Zhao, Feng-Zhen
core   +1 more source

Lorentzian polynomials on cones

Forum of Mathematics, Sigma
Inspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one.
Petter Brändén, Jonathan Leake
doaj   +1 more source

Zeros distribution and interlacing property for certain polynomial sequences

Open Mathematics
In this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
doaj   +1 more source

Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy

Forum of Mathematics, Pi
Describing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy ...
Swee Hong Chan, Igor Pak
doaj   +1 more source

Interlacing Log-concavity of the Boros-Moll Polynomials [PDF]

, 2010
We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$.
Chen, William Y. C., Wang, Larry X. W., Xia, Ernest X. W.   +2 more
core  

Stanley's Major Contributions to Ehrhart Theory

, 2015
This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra.
Beck, Matthias
core   +1 more source