Stirling Pairs of Permutations

Brualdi, Richard A.

doi:10.1007/s00373-020-02172-x

Cited by 9 publications

(14 citation statements)

References 8 publications

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“…In this paper, we build upon the assumption of N P = P [5,6,7], improve the recent theoretical results of the branch and bound algorithm (B&B) [35,36], integrating generating function approaches [37,38], introduce a new reduction method and an improved mutation operator (IMO). Simultaneously, the method is applicable in computing an upper bound of the mutation probability for the 0-1 KP, as well as in constructing a counterexample where the mutation probability does not tend toward 0 with an increasing number of decision variables [25].…”

Section: Our Resultsmentioning

confidence: 99%

Community Participation Strategy for Sustainable Urban Regeneration in Xiamen, China

Yang

2022

Land

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Urban regeneration is an important strategic choice in promoting urban development globally. Existing research on urban regeneration mainly focuses on the community’s economic benefits. However, less research concentrates on how community participation contributes to the sustainable development of communities. The aim of this study is to explore the community regeneration approach in the context of urban regeneration in a typical village community in China. This study finds that participatory planning, which is mainly characterized by public participation, can be an effective way of communication and cooperation. The collaborative workshops provide a participatory platform for stakeholders and promote sustainable community development. Therefore, traditional planning approaches may need to be changed. The contribution of this article is to develop a collaborative planning approach for sustainable community development, which can serve as a reference for community governance in China and other developing countries.

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Section: Our Resultsmentioning

confidence: 99%

Community Participation Strategy for Sustainable Urban Regeneration in Xiamen, China

Yang

2022

Land

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“…Let falsefalse{λifalsefalse}i=1r denote the eigenvalues of ρ. By Pólya’s enumeration theorem [35,36], we can interpret (4.1) as a generating function for the number of non-equivalent colourings of a set S with the r colours falsefalse{λifalsefalse}i=1r. The role of G here is to define the equivalence between colourings through its action on S.…”

Section: Generalization Of the Algorithmmentioning

confidence: 99%

Cycle index polynomials and generalized quantum separability tests

2023

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The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled one. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance probability of such tests as the number of copies of the state becomes larger. We prove that the analytical form of this expression is given by the cycle index polynomial of the symmetric group S k , which is itself related to the Bell polynomials. After doing so, we derive a family of quantum separability tests, each of which is generated by a finite group; for all such algorithms, we show that the acceptance probability is determined by the cycle index polynomial of the group. Finally, we produce and analyse explicit circuit constructions for these tests, showing that the tests corresponding to the symmetric and cyclic groups can be executed with O ( k 2 ) and O ( k log ⁡ ( k ) ) controlled-SWAP gates, respectively, where k is the number of copies of the state being tested.

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“…(3) There is a resolvable transversal design RTD(k − 1, 1; n). 2.2 Relevant definitions of key sharing scheme Definition 2.8 [15] Let k, n be positive integers and 2 ≤ k ≤ n. P = {P 1 , P 2 , • • • , P n } is a set of cardinality n, and the elements in P are called participants. Let S be the secret space and M be the share space.…”

Section: Relevant Definitions Of Combinatorial Designmentioning

confidence: 99%

Combinatorial Construction of Repairable Threshold Key Sharing Schemes

Wang

Jin

Deng

2023

Preprint

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In this paper, we use two types of designs to construct repairable threshold schemes, and calculate information rate and communication complexity of the schemes to analyze their performance. Firstly, SB(2λ + 1, λ, 4λ + 3) is used to construct the (3, 4λ + 3, 2λ + 1)−RTS, which is based on (3λ + 3, 4λ + 4)−Shamir threshold scheme. Secondly, the mutually orthogonal Latin squares are constructed, and a RTD(q, 1; q 2) is obtained by them. Further, the RB(q, 1; q 3) is obtained through filling hole method. (2, n, q)−RTS based on (q, 2q − 1, q 3)−Ramp threshold scheme and (3, n, q)−RTS based on (2q, 3q − 3, q 3)−Ramp threshold scheme are constructed by RB(q, 1; q 3), where 2q 2 ≤ n ≤ q 2 (q 2 + q + 1). Finally , the information rate and the communication complexity of three repairable threshold schemes are calculated, and the performance of these schemes is analyzed. Compared with the existing schemes, the results show that (2, n, q)−RTS and (3, n, q)−RTS constructed by RB(q, 1; q 3) have higher information rate and lower communication complexity.

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Stirling Pairs of Permutations

Cited by 9 publications

References 8 publications

Community Participation Strategy for Sustainable Urban Regeneration in Xiamen, China

Community Participation Strategy for Sustainable Urban Regeneration in Xiamen, China

Cycle index polynomials and generalized quantum separability tests

Combinatorial Construction of Repairable Threshold Key Sharing Schemes

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