Hyperdeterminants on semilattices

We compute hyperdeterminants of hypermatrices whose indices belongs in a meet-semilattice and whose entries depend only of the greatest lower bound of the indices. One shows that an elementary expansion of such a polynomial allows to generalize a theorem of Lindstr\"om to higher-dimensional determinants. And we gave as an application generalizations of some results due to Lehmer, Li and Haukkanen.Comment: New version of "A remark about factorizing GCD-type Hyperdeterminants". Title changed. Results, examples and remarks adde

r−r-Bell polynomials in combinatorial Hopf algebras

We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.Comment: 7 page

Clustering properties of rectangular Macdonald polynomials

The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials. The present paper is devoted to the proof of this formula. To this aim we use four families of Jack/Macdonald polynomials: symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted nonsymmetric.Comment: 43 pages, 2 figure

Noncommutative Symmetric Functions Associated with a Code, Lazard Elimination, and Witt Vectors

The construction of the universal ring of Witt vectors is related to Lazard's factorizations of free monoids by means of a noncommutative analogue. This is done by associating to a code a specialization of noncommutative symmetric functions

Parallel Hybrid Trajectory Based Metaheuristics for Real-World Problems

G. Luque, E. Alba, Parallel Hybrid Trajectory Based Metaheuristics for Real-World Problems, In Proceedings of Intelligent Networking and Collaborative Systems, pp. 184-191, 2-4 September, 2015, Taipei, Taiwan, IEEE PressThis paper proposes a novel algorithm combining path relinking with a set of cooperating trajectory based parallel algorithms to yield a new metaheuristic of enhanced search features. Algorithms based on the exploration of the neighborhood of a single solution, like simulated annealing (SA), have offered accurate results for a large number of real-world problems in the past. Because of their trajectory based nature, some advanced models such as the cooperative one are competitive in academic problems, but still show many limitations in addressing large scale instances. In addition, the field of parallel models for trajectory methods has not deeply been studied yet (at least in comparison with parallel population based models). In this work, we propose a new hybrid algorithm which improves cooperative single solution techniques by using path relinking, allowing both to reduce the global execution time and to improve the efficacy of the method. We applied here this new model using a large benchmark of instances of two real-world NP-hard problems: DNA fragment assembly and QAP problems, with competitive results.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the self-convolution of generalized Fibonacci numbers

We focus on a family of equalities pioneered by Zhang and generalized by Zao and Wang and hence by Mansour which involves self convolution of generalized Fibonacci numbers. We show that all these formulas are nicely stated in only one equation involving a bivariate ordinary generating function and we give also a formula for the coefficients appearing in that context. As a consequence, we give the general forms for the equalities of Zhang, Zao-Wang and Mansour

Math Oracles: A New Way of Designing Efficient Self-Adaptive Algorithms

In this paper we present a new general methodology to develop self-adaptive methods at a low computational cost. Instead of going purely ad-hoc we de ne several simple steps to include theoretical models as additional information in our algorithm. Our idea is to incorporate the predictive information (future behavior) provided by well-known mathematical models or other prediction systems (the oracle) to build enhanced methods. We show the main steps which should be considered to include this new kind of information into any algorithm. In addition, we actually test the idea on a speci c algorithm, a genetic algorithm (GA). Experiments show that our proposal is able to obtain similar, or even better results when it is compared to the traditional algorithm. We also show the bene ts in terms of saving time and a lower complexity of parameter settings.Universidad de Málaga. Proyecto roadME (TIN2011-28194