相关论文: Largest values of the Stern sequence, alternating …

The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives…

We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic…

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of…

Scalar-tensor~(ST) theories of gravity are natural phenomenological extensions to general relativity. Although these theories are severely constrained both by solar system experiments and by binary pulsar observations, a large set of ST…

We study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more general "d-refined" enumerations of ASMs according to the first…

For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e. we provide exact and explicit expressions for its normal form which has all a's to the…

Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation…

Stellar systems consisting of three or more stars are not an uncommon occurrence in the Galaxy. Nearly 50% of solar-type wide binaries with separations >1000 au are actually higher-order multiples with one component being a close binary.…

We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…

The Euler number $E_n$ (resp. Entringer number $E_{n,k}$) enumerates the alternating (down-up) permutations of $\{1,\dots,n\}$ (resp. starting with $k$). The Springer number $S_n$ (resp. Arnold number $S_{n,k}$) enumerates the type $B$…

Let $\mathcal{F}\subset\binom{[n]}{k}$ be an intersecting family. For an element $i\in[n]$, the degree of $i$ is the number of sets in $\mathcal{F}$ that contain $i$. Assume that the degrees are ordered as $d_{1}\ge d_{2}\ge\cdots\ge…

A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken large enough and the result gives rise to the Borel…

Following a suggestion by Gasperini and Veneziano, that String Cosmology can be reconciled with Inflation and, hence, with the Standard Big Bang, we display an analytical solution which possesses four interesting properties: (1) it is…

In this paper, we have constructed the higher order k-bonacci matrices and studied some of their basic properties. We have also shown that these matrices satisfying some new and interesting relations in k-bonacci recurrence. This is the…

Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order…

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…

We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficiently large annulus, for which the $\ell^2$ norm of the…

We construct orthogonal arrays OA$_{\lambda} (k,n)$ (of strength two) having a row that is repeated $m$ times, where $m$ is as large as possible. In particular, we consider OAs where the ratio $m / \lambda$ is as large as possible; these…

We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…

We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is…