Related papers: Scaled Arndt Compositions
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. In their original paper they developed formulas, generating…
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields…
The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition.…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output…
Motivated by scalar-tensor gravities, we consider a theory which contains massless scalar fields with different sound speeds. We derive unitarity relations for partial wave amplitudes of $2 \to 2$ scattering, with explicit formulas for…
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for triangulated categories. We study composition series of derived…
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
The constituent counting rules, i.e., the scaling behavior of amplitudes (in terms of the number of fundamental constituents) for exclusive processes when high energy scales are present, have been known for decades, and have been borne out…
Compositional generalization is a basic mechanism in human language learning, which current neural networks struggle with. A recently proposed Disentangled sequence-to-sequence model (Dangle) shows promising generalization capability by…
We continue the work of Eriksen, Freij, and Wastlund [3], who study derangements that descend in blocks of prescribed lengths. We generalize their work to derangements that ascend in some blocks and descend in others. In particular, we…
RO*-algebras are defined and studied. For RO*-algebra T, using properties of partial order, it is established that the set of bounded elements can be endowed with C*-norm. The structure of commutative subalgebras of T is considered and the…
For a nonnegative self-adjoint operator $A_0$ acting on a Hilbert space $\mathfrak{H}$ singular perturbations of the form $A_0+V, \ V=\sum_{1}^{n}{b}_{ij}<\psi_j,\cdot>\psi_i$ are studied under some additional requirements of symmetry…
Using Pascal triangle, we give a simple generalization to the so-called STRAND Puzzle solved by Srinivasa Ramanujan. Thus we are interested in computing the median, first and third quartiles of some integer valued distributions, arising…
The classical involutive division theory by Janet decomposes in the same way both the ideal and the escalier. The aim of this paper, following Janet's approach, is to discuss the combinatorial properties of involutive divisions, when…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…