On Refinements of Wilf-Equivalence for Involutions

Yan, Sherry H. F.; Wang, Lintong; Zhou, Robin D. P.

doi:10.48550/arxiv.2212.01800

Cited by 1 publication

(9 citation statements)

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“…Recall that when we set λ to be the n by n square diagram, the transversal T ∈ ST λ becomes an involution π in I n with Peak(π) = Peak(T ) and Val(π) = Val(T ). Hence, the following result follows directly from Theorem 1.6, confirming a recent conjecture posed by Yan-Wang-Zhou [38].…”

Section: Introductionsupporting

confidence: 84%

“…Note that the case k = 3 of Theorem 1.6 has been verified by Yan-Wang-Zhou [38] by establishing a peak set preserving bijection between ST λ (J 3 ⊕τ ) and ST λ (I 3 ⊕τ ).…”

Section: Introductionmentioning

confidence: 80%

“…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: 93%

“…As a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern avoiding permutations and various interesting results on them have been obtained in the literature (see e.g. [2,3,12,17,19,38,39]). This paper is devoted to the investigation of the distribution of the peak set and the valley set on standard Young tableaux and pattern avoiding transversals.…”

Section: Introductionmentioning

confidence: 99%

“…This is actually the motivation and original intention behind our writing of this article. The equiditribution of permutation statistics on pattern avoiding permutations and transversals has been investigated in recent literature, see [7,8,9,13,16,37,38,39] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

2021

School Mathematics Textbooks in China

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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: Introductionsupporting

confidence: 84%

“…Note that the case k = 3 of Theorem 1.6 has been verified by Yan-Wang-Zhou [38] by establishing a peak set preserving bijection between ST λ (J 3 ⊕τ ) and ST λ (I 3 ⊕τ ).…”

Section: Introductionmentioning

confidence: 80%