Pattern avoiding alternating involutions

Barnabei, Marilena; Bonetti, Flavio; Castronuovo, Niccolò; Silimbani, Matteo

doi:10.54550/eca2023v3s1r4

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…Recently, Yan-Wang-Zhou [38] proved that AI n (I 3 ⊕ τ ) = AI n (J 3 ⊕ τ ) for any nonempty permutation τ as conjectured by Barnabei-Bonetti-Castronuovo-Silimbani [5]. In this paper, we shall obtain the following extension of the result of Yan-Wang-Zhou to general k. Theorem 1.8 Let n, k ≥ 1.…”

Section: Introductionmentioning

confidence: 78%

“…They enumerated and characterized some classes of alternating involutions avoiding a single pattern of length 4. Furthermore, Barnabei-Bonetti-Castronuovo-Silimbani [5] posed several conjectures concerning pattern avoiding alternating involutions, which have been confirmed by Yan-Wang-Zhou [38] and Zhou-Yan [39].…”

Section: Introductionmentioning

confidence: 92%

“…Barnabei-Bonetti-Castronuovo-Silimbani [5] initiated the enumeration of pattern avoiding alternating involutions [5]. They enumerated and characterized some classes of alternating involutions avoiding a single pattern of length 4.…”

Section: Introductionmentioning

confidence: 99%

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International Comparison on the Application of Information Technology in High School Mathematics Textbooks

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Ultra-dense networks are widely regarded as a promising solution to explosively growing applications of Internet-of-Things (IoT) mobile devices (IMDs). However, complicated and severe interferences need to be tackled properly in such networks. To this end, both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are utilized at first. Then, in order to attain a goal of green and secure computation offloading, under the proportional allocation of computational resources and the constraints of latency and security cost, joint device association, channel selection, security service assignment, power control and computation offloading are done for minimizing the overall energy consumed by all IMDs. It is noteworthy that multi-step computation offloading is concentrated to balance the network loads and utilize computing resources fully. Since the finally formulated problem is in a nonlinear mixed-integer form, it may be very difficult to find its closed-form solution. To solve it, an improved whale optimization algorithm (IWOA) is designed. As for this algorithm, the convergence, computational complexity and parallel implementation are analyzed in detail. Simulation results show that the designed algorithm may achieve lower energy consumption than other existing algorithms under the constraints of latency and security cost.

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 92%