Related papers: Largest values of the Stern sequence, alternating …

When one inserts a number of identical bars in between blocks of an ordered set partition, they get a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred…

For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed…

In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…

We would like to investigate the information contained in our observations and to what extent each of them contributes individually to constraining the physical parameters of the system we are investigating. To do this, we present a study…

A de Bruijn sequence of order n over a k-symbol alphabet is a circular sequence where each length-n sequence occurs exactly once. We present a way of extending de Bruijn sequences by adding a new symbol to the alphabet: the extension is…

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii)…

We show that the largest character degree of an alternating group $A_n$ with $n\geq 5$ can be bounded in terms of smaller degrees in the sense that \[ b(A_n)^2<\sum_{\psi\in\textrm{Irr}(A_n),\,\psi(1)< b(A_n)}\psi(1)^2, \] where…

We look at a class of transcendental real numbers xi which, together with their square, satisfy some extremal property of simultaneous approximation by rational numbers with the same denominator. We give a sufficient condition for such a…

We study the effect of time evolution on galaxy bias. We argue that at any order in perturbations, the galaxy density contrast can be expressed in terms of a finite set of locally measurable operators made of spatial and temporal…

Massive stars are among the most important objects in the Universe and many (most?) of them are formed in binaries. A selection of observational and theoretical facts that illustrate the importance of binaries and the evolution of massive…

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a…

Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and…

We discuss the dominant terms of the relativistic galaxy number counts to second order in cosmological perturbation theory on sub-Hubble scales and on intermediate to large redshifts. In particular, we determine their contribution to the…

We study the structure of relativistic stars in $\mathcal{R}+\alpha \mathcal{R}^{2}$ theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature…

Given an integer $n$, we introduce the integral Lie ring of partitions with bounded maximal part, whose elements are in one-to-one correspondence to integer partitions with parts in $\{1,2,\dots, n-1\}$. Starting from an abelian subring, we…

A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the…

We present the classical Stern-Brocot tree and provide a new proof of the fact that every rational number between 0 and 1 appears in the tree. We then generalize theStern-Brocot tree to allow for arbitrary choice of starting terms, and…

Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…

We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…