On two classes of permutations with number-theoretic conditions on the lengths of the cycles

Let Λ be an arbitrary set of positive integers andS _n (Λ) the set of all permutations of degreen for which the lengths of all cycles belong to the set Λ. In the paper the asymptotics of the ratio |S _n (Λ)|/n! asn→∞ is studied in the following cases: 1) Λ is the union of finitely many arithmetic progressions, 2) Λ consists of all positive integers that are not divisible by any number from a given finite set of pairwise coprime positive integers. Here |S _n (Λ)| stands for the number of elements in the finite setS _n (Λ). Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 881–891, December, 1997. Translated by A. I. Shtern     

全错位排列问题的基于芯片的DNA计算模型

全错位排列问题作为组合数学中一个重要的问题,到目前为止还没有好的算法.应用DNA芯片技术,提出了全错位排列问题的基于芯片的DNA计算模型,并对模型进行了简要分析.     

关于多项式函数的计数

Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.     

Explicitly correlated MRCI-F12 potential energy surfaces for methane fit with several permutation invariant schemes and full-dimensional vibrational calculations

A data-set of nearly 100,000 symmetry unique multi-configurational ab initio points for methane were generated at the (AE)-MRCI-F12(Q)/CVQZ-F12 level, including energies beyond 30,000 cm^?1 above the minimum and fit into potential energy surfaces (PESs) by several permutation invariant schemes. A multi-expansion interpolative fit combining interpolating moving least squares (IMLS) fitting and permutation invariant polynomials (PIP) was able to fit the complete data-set to a root-mean-square deviation of 1.0 cm^?1 and thus was used to benchmark the other fitting methods. The other fitting methods include a single PIP expansion and two neural network (NN) based approaches, one of which combines NN with PIP. Full-dimensional variational vibrational calculations using a contracted-iterative method (and a Lanczos eigensolver) were used to assess the spectroscopic accuracy of the electronic structure method. The results show that the NN-based fitting approaches are able to fit the data-set remarkably accurately with the PIP–NN method producing levels in remarkably close agreement with the PIP–IMLS benchmark. The (AE)-MRCI-F12(Q)/CVQZ-F12 electronic structure method produces vibrational levels of near spectroscopic accuracy and a superb equilibrium geometry. The levels are systematically slightly too high, beginning at ～ 1–2 cm^?1 above the fundamentals and becoming correspondingly higher for overtones. The PES is therefore suitable for small ab initio or empirical corrections and since it is based on a multi-reference method, can be extended to represent dynamically relevant dissociation channels.     

Polynomial algorithms for kernels in comparability, permutation and P 4-free graphs

In this paper, we give three polynomial algorithms which detect a kernel in comparability graphs relatively to an M-orientation, in permutation graphs and in P₄-free graphs with a normal orientation. MSC classification: 05C69, 05C85 Correspondence to: Saoula Youcef     

Young Straightening in a Quotient Sn-Module

We describe a straightening algorithm for the action of S _n on a certain graded ring . The ring appears in the work of C. de Concini and C. Procesi [2] and T. Tanisaki [8], and more recently in the work of A. Garsia and C. Procesi [4]. This ring is a graded version of the permutation representation resulting from the action of S _n on the left cosets of a Young subgroup. As a corollary of our straightening algorithm we obtain a combinatorial proof of the fact that the top degree component of affords the irreducible representation of S _n indexed by .     

The Numbers of Permutation Groups Orbits and of the Wreath Product Orbits

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保守超混沌在数字图像加密中的应用

基于保守超混沌信号,提出一种数字图像加密算法.该算法利用一个5维保守超混沌系统产生5通道时间序列对原图像分别进行RGB三基色像素级和比特级置乱,再对置乱的RGB三基色作异或操作.在此基础上,利用其中一个通道的时间序列作为密钥分别进行一次正向异或操作的扩散和S盒处理,一次反向异或操作的扩散与S盒处理及置乱,得到加密的图像.最后利用直方图、信息熵、密钥空间等安全性指标对该加密算法进行测试,并与一个五维耗散超混沌系统应用于图像加密的实例进行对比.数值结果表明保守混沌应用到数字图像加密的算法具有更高的安全性和可靠性.     

Infinitely Divisible Limit Processes for the Ewens Sampling Formula

The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Using techniques from probabilistic number theory, it is shown that, under very general conditions, a partial sum process weakly converges in a function space if and only if the corresponding process defined through sums of independent random variables weakly converges. As a consequence of this result, necessary and sufficient conditions for weak convergence to a stable process are established. A counterexample showing that these conditions are not necessary for the one-dimensional convergence is presented. Very few results on the necessity part are known in the literature.     

Machine learning and signed particles,an alternative and efficient way to simulate quantum systems

Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi-dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.