Related papers: Counting or producing all fixed cardinality transv…
We obtain a complete and minimal set of 170 generators for the algebra of $SL(2,\C)^{\times 4}$-covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties…
We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on…
We propose new algorithms for generating $k$-statistics, multivariate $k$-statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up…
We compare two methods for evaluating the cardinality of the Cartesian product $N \times N$ of the set of natural numbers $N$. The first is used to explain the thermodynamics of black body radiation by using convergent functions on $N…
Cardinality estimation algorithms receive a stream of elements, with possible repetitions, and return the number of distinct elements in the stream. Such algorithms seek to minimize the required memory and CPU resource consumption at the…
Model counting is the problem of computing the number of satisfying assignments of a given propositional formula. Although exact model counters can be naturally furnished by most of the knowledge compilation (KC) methods, in practice, they…
Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
Any Schur ring is uniquely determined by a partition of the elements of the group. In this paper we present a general technique for enumerating Schur rings over cyclic groups using traditional Schur rings. We also survey recent efforts to…
We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different…
We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
Considered will be properties of the set of real numbers $\Re$ generated by an operator that has form of an exponential function of Gelfond-Schneider type with rational arguments. It will be shown that such created set has cardinal number…
We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.