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1. Cyclic Sieving for cyclic codes

   https://doi.org/10.1016/j.ffa.2021.101846  

   Mason, Alex; Reiner, Victor; Sridhar, Shruthi (August 2021, Finite Fields and Their Applications)
2. Impact of Multiple Cyclic Loads on the Cyclic and Post-Cyclic Behavior of Fine-Grained Soils

   https://doi.org/10.1061/9780784485316.010  

   Kiuna, Veronica; Ajmera, Beena; Tiwari, Binod (February 2024, American Society of Civil Engineers)

   Fine-grained soils subjected to seismic loading often exhibit instability or failure of slopes, foundations, and embankments. To understand the behavior of clay soils under multiple earthquake loads, kaolinite samples were prepared and tested in the laboratory using a cyclic simple shear device. Each sample was subjected to two cyclic events separated by different degrees of reconsolidation periods to simulate different levels of excess pore water pressure dissipation. The results indicated that the degree to which excess pore water pressure generated during the first cyclic event was dissipated affected the cyclic resistance of the soil during the second cyclic event. The post-cyclic undrained shear strength was also found to be a function of the degree to which excess pore water pressure from the first cyclic load was allowed to dissipate prior to the application of the second cyclic load. 

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3. Cyclic Shuffle-Compatibility Via Cyclic Shuffle Algebras

   https://doi.org/10.1007/s00026-023-00669-9  

   Liang, Jinting; Sagan, Bruce_E; Zhuang, Yan (October 2023, Annals of Combinatorics)

   Abstract A permutation statistic$${{\,\textrm{st}\,}}$$ $\text{st}$is said to be shuffle-compatible if the distribution of$${{\,\textrm{st}\,}}$$ $\text{st}$over the set of shuffles of two disjoint permutations$$\pi $$ $\pi$and$$\sigma $$ $\sigma$depends only on$${{\,\textrm{st}\,}}\pi $$ $\text{st}\pi$,$${{\,\textrm{st}\,}}\sigma $$ $\text{st}\sigma$, and the lengths of$$\pi $$ $\pi$and$$\sigma $$ $\sigma$. Shuffle-compatibility is implicit in Stanley’s early work onP-partitions, and was first explicitly studied by Gessel and Zhuang, who developed an algebraic framework for shuffle-compatibility centered around their notion of the shuffle algebra of a shuffle-compatible statistic. For a family of statistics called descent statistics, these shuffle algebras are isomorphic to quotients of the algebra of quasisymmetric functions. Recently, Domagalski, Liang, Minnich, Sagan, Schmidt, and Sietsema defined a version of shuffle-compatibility for statistics on cyclic permutations, and studied cyclic shuffle-compatibility through purely combinatorial means. In this paper, we define the cyclic shuffle algebra of a cyclic shuffle-compatible statistic, and develop an algebraic framework for cyclic shuffle-compatibility in which the role of quasisymmetric functions is replaced by the cyclic quasisymmetric functions recently introduced by Adin, Gessel, Reiner, and Roichman. We use our theory to provide explicit descriptions for the cyclic shuffle algebras of various cyclic permutation statistics, which in turn gives algebraic proofs for their cyclic shuffle-compatibility. 

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4. Cyclic Polyacetylene

   https://doi.org/10.1038/s41557-021-00713-2  

   Miao, Z.; Gonsales, S. A.; Ehm, C.; Mentink-Vigier, F.; Bowers, C. R.; Sumerlin, B. S.; Veige, A. S. (June 2021, Nature chemistry)
5. Minimal descriptions of cyclic memories

   https://doi.org/10.1098/rspa.2018.0874  

   Paulsen, Joseph D.; Keim, Nathan C. (June 2019, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)