Related papers: Scaled Arndt Compositions
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…
For fixed positive reals $t$ and $\alpha$, consider the sequence $S_t(\alpha) = (s_1, s_2, \ldots, )$ with $s_n = \left \lfloor t\alpha^n \right \rfloor$. In 1964, Graham managed to characterize those pairs $(t, \alpha)$ with $0 < t < 1$…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group $S_n$ in order to construct recurrence relations for enumerating certain subsets of $S_n$. Occasionally one can find `closed form'…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in arXiv:1307.0967. We establish by cut-and-join methods that the number of partial chord diagrams…
Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…
We describe a new method that is both physically explicable and quantitatively accurate in describing the multifractal characteristics of intermittent events based on groupings of rank-ordered fluctuations. The generic nature of such…
We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
We introduce "chain by chain" method for constructing the constraint structure of a system possessing both first and second class constraints. We show that the whole constraints can be classified into completely irreducible first or second…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \geq 1$, a symmetrically constrained composition $\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by R.J.Evans in 1981 and, following an elegant idea of G.W.Anderson in 1991 they were…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…