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1. Doppelgängers: Bijections of Plane Partitions

   https://doi.org/10.1093/imrn/rny018  

   Hamaker, Zachary; Patrias, Rebecca; Pechenik, Oliver; Williams, Nathan (March 2018, International Mathematics Research Notices)

   null (Ed.)

   Abstract We say two posets are doppelgängers if they have the same number of P-partitions of each height k. We give a uniform framework for bijective proofs that posets are doppelgängers by synthesizing K-theoretic Schubert calculus techniques of H. Thomas and A. Yong with M. Haiman’s rectification bijection and an observation of R. Proctor. Geometrically, these bijections reflect the rational equivalence of certain subvarieties of minuscule flag manifolds. As a special case, we provide the 1st bijective proof of a 1983 theorem of R. Proctor—that plane partitions of height k in a rectangle are equinumerous with plane partitions of height k in a shifted trapezoid. 

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2. Out-of-plane chiral domain wall spin-structures in ultrathin in-plane magnets

   https://doi.org/10.1038/ncomms15302  

   Chen, Gong; Kang, Sang Pyo; Ophus, Colin; N’Diaye, Alpha T.; Kwon, Hee Young; Qiu, Ryan T.; Won, Changyeon; Liu, Kai; Wu, Yizheng; Schmid, Andreas K. (May 2017, Nature Communications)
3. Magnetic relaxation in epitaxial films with in-plane and out-of-plane anisotropies

   https://doi.org/10.1007/s00339-023-06974-7  

   Lisfi, Abdellah; Efe, Frank; Wuttig, Manfred (October 2023, Applied Physics A)
4. Resolving in-plane and out-of-plane mobility using time resolved microwave conductivity

   https://doi.org/10.1039/D0TC00328J  

   Chattopadhyay, Shirsopratim; Kokenyesi, Robert S.; Hong, Min Ji; Watts, C Lowell; Labram, John G. (August 2020, Journal of Materials Chemistry C)

   null (Ed.)

   The contactless characterization technique time resolved microwave conductivity (TRMC) provides a means to rapidly and unambiguously approximate carrier mobilities and lifetimes for a variety of semiconducting materials. When using a cavity-based approach however, the technique can conventionally only resolve carrier mobilities in the plane of the substrate. In solar cells, charge carriers are extracted in the direction perpendicular to the substrate, therefore it would be beneficial if one were able to evaluate the mobility in this direction also. Here we present a novel approach for resolving charge carrier mobilities in different planes within a sample. Using a range of 3D-printed sample holders, where the sample is held at various angles relative to the incident light, we are able to simultaneously resolve the mobility in the plane of the sample and out of the plane of the sample. As examples, we have studied the 3-dimensional corner-connected metal halide perovskite methylammonium lead iodide and the 2-dimensional perovskite precusor, lead iodide. 

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5. Bijective Cremona transformations of the plane

   https://doi.org/10.1007/s00029-022-00768-0  

   Asgarli, Shamil; Lai, Kuan-Wen; Nakahara, Masahiro; Zimmermann, Susanna (July 2022, Selecta Mathematica)