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In Many Circles. Permutations as Products of Cycles.
Published in Miklós Bóna, Combinatorics of Permutations, 2022
The symmetric group is a quintessential ingredient of group theory. It is well known, for instance, that every finite group of n elements is a subgroup of Sn. Extensive research of the symmetric group is therefore certainly justified. In this chapter, we will concentrate on the enumerative combinatorics of the symmetric group, that is, we are going to count permutations according to statistics that are relevant to this second way of looking at them.
Algebraic Structures I (Matrices, Groups, Rings, and Fields)
Published in R. Balakrishnan, Sriraman Sridharan, Discrete Mathematics, 2019
R. Balakrishnan, Sriraman Sridharan
[After the French mathematician J. L. Lagrange]Lagrange The order of any subgroup of a finite group G divides the order of G.
Poisson degenerate central moments related to degenerate Dowling and degenerate r-Dowling polynomials
Published in Applied Mathematics in Science and Engineering, 2022
Taekyun Kim, Dae San Kim, Hye Kyung Kim
A finite lattice L is geometric if it is a finite semimodular lattice which is also atomic. Dowling constructed an important finite geometric lattice out of a finite set of n elements and a finite group G of order m, called Dowling lattice of rank n over a finite group of order m. If L is the Dowling lattice of rank n over a finite group G of order m, then the Whitney numbers of the first kind and the Whitney numbers of the second kind are respectively denoted by and . The Whitney numbers and satisfy the following Stirling number-like relations: For , Dowling polynomials are given by
Extremal inverse eigenvalue problem for irreducible acyclic matrices
Published in Applied Mathematics in Science and Engineering, 2022
Debashish Sharma, Bhaba Kumar Sarma
Throughout this paper, the term graph will mean an undirected graph on the vertex set without loops or multiple edges. Let and be two graphs on V. A permutation π of V is an isomorphism of onto , if is an edge in if and only if is an edge in . If such a π exists, and are said to be isomorphic. If , then the isomorphism π is called an automorphism of G. The set of automorphisms of G form a finite group, denoted by .
Accurate screw detection method based on faster R-CNN and rotation edge similarity for automatic screw disassembly
Published in International Journal of Computer Integrated Manufacturing, 2021
Xinyu Li, Ming Li, Yongfei Wu, Daoxiang Zhou, Tianyu Liu, Fang Hao, Junhong Yue, Qiyue Ma
In addition, to overcome the shortcomings of the existing screw location methods, while considering the deep learning and finite group theory as the foundation, in this study, the authors propose an accurate screw location method by combining the Faster R-CNN and innovative RSE. Because Faster R-CNN can identify tiny targets from complex images, it is first preliminarily applied to provide the locations and classifications of screws on MPMs. However, the resultant accuracy of Faster R-CNN cannot satisfy the needs of automated screw disassembly; therefore, the RES method is additionally incorporated to adjust the location and correct the classification of screws provided by Faster R-CNN. Correspondingly, the relevant literature reviews are tabulated in Table 1.