In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

We investigate the limit of sequences vertex algebras. discuss under what condition vector space direct such a sequence is again algebra. then apply this framework to permutation orbifolds operator algebras and their large N limit. establish that for any nested oligomorphic orbifold exists, we give necessary sufficient factorize. This helps clarify question VOAs are candidates holographic confo...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

An iterative formula for the Green polynomial is given using vertex operator realization of Hall-Littlewood function. Based on this, (1) a general combinatorial given; (2) several compact formulas are Green's polynomials associated with upper partitions length $\leq 3$ and diagonal lengths 3$; (3) Murnaghan-Nakayama type obtained; (4) an derived bitrace finite linear group $G$ Iwahori-Hecke alg...

Abstract. Given a partition λ = (λ1, λ2, . . . λk), let λ rc = (λ2 − 1, λ3 − 1, . . . λk − 1). It is easily seen that the diagram λ/λ is connected and has no 2 × 2 subdiagrams which we shall refer to as a ribbon. To each ribbon R, we associate a symmetric function operator S. We may define the major index of a ribbon maj(R) to be the major index of any permutation that fits the ribbon. This pap...

In this work we present an application of the Confidence Interval Based Crossover using L2 Norm (CIXL2) and BLX-α crossovers to the evolution of neural networks. CIXL2 is a new crossover operator, based on obtaining the statistical features of the best individuals of the population. These features are used as virtual parents for the crossover operator. Due to the permutation problem of neural n...

The classical approach of solvability using group theory is well known and one original motivation is to solve polynomials by radicals. Radicals are square, cube, square root, cube root etc of the original coefficients for the polynomial. A polynomial is solvable by radicals if the permutation group is solvable. This is exact solvability via group theory. With modern computers, we might need to...

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobserv...