@article {JYS1, AUTHOR = {Shi, Jian Yi}, TITLE = {Alcoves corresponding to an affine {W}eyl group}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {35}, YEAR = {1987}, NUMBER = {1}, PAGES = {42--55}, doi = {10.1112/jlms/s2-35.1.42} } @article {JYS2, AUTHOR = {Shi, Jian Yi}, TITLE = {Sign types corresponding to an affine {W}eyl group}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {35}, YEAR = {1987}, NUMBER = {1}, PAGES = {56--74}, doi = {10.1112/jlms/s2-35.1.56} } @article {JYS3, AUTHOR = {Shi, Jian Yi}, TITLE = {On two presentations of the affine {W}eyl groups of classical types}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {221}, YEAR = {1999}, NUMBER = {1}, PAGES = {360--383}, doi = {10.1006/jabr.1999.8000} } @book {BOURB, AUTHOR = {Bourbaki, N.}, TITLE = {\'{E}l\'{e}ments de math\'{e}matique. {F}asc. {XXXIV}. {G}roupes et alg\`ebres de {L}ie. {C}hapitre {IV}: {G}roupes de {C}oxeter et syst\`emes de {T}its. {C}hapitre {V}: {G}roupes engendr\'{e}s par des r\'{e}flexions. {C}hapitre {VI}: syst\`emes de racines}, SERIES = {Actualit\'{e}s Scientifiques et Industrielles, No. 1337}, PUBLISHER = {Hermann, Paris}, YEAR = {1968}, PAGES = {288 pp. (loose errata)}, } @article{dyer2016small, title={Small roots, low elements, and the weak order in Coxeter groups}, author={Dyer, M. and Hohlweg, C.}, fjournal={Advances in Mathematics}, journal = {Adv. Math.}, volume={301}, pages={739--784}, year={2016}, publisher={Elsevier}, doi={10.1016/j.aim.2016.06.022} } @book {MR2133266, AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco}, TITLE = {Combinatorics of {C}oxeter groups}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {231}, PUBLISHER = {Springer, New York}, YEAR = {2005}, PAGES = {xiv+363}, } @article {NC1, AUTHOR = {Chapelier-Laget, Nathan}, TITLE = {Shi variety variety corresponding to an affine Weyl group}, journal = {arXiv preprint: 2010.04310}, year = {2020}, } @article {NC_Thesis, AUTHOR = {Chapelier-Laget, Nathan}, TITLE = {Variétés de Shi associées aux groupes de Weyl affines}, journal = {Ph.D. thesis}, year = {2021}, } @article{athanasiadis1999simple, title={A simple bijection for the regions of the Shi arrangement of hyperplanes}, author={Athanasiadis, Christos A and Linusson, Svante}, fjournal={Discrete mathematics}, journal = {Discrete Math.}, volume={204}, number={1-3}, pages={27--39}, year={1999}, publisher={Elsevier}, doi={10.1016/S0012-365X(98)00365-3} } @article{armstrong2015parking, title={Parking spaces}, author={Armstrong, Drew and Reiner, Victor and Rhoades, Brendon}, fjournal={Advances in Mathematics}, journal = {Adv. Math.}, volume={269}, pages={647--706}, year={2015}, publisher={Elsevier}, doi={10.1016/j.aim.2014.10.012} } @article{reiner1997non, title={Non-crossing partitions for classical reflection groups}, author={Reiner, Victor}, fjournal={Discrete Mathematics}, journal = {Discrete Math.}, volume={177}, number={1-3}, pages={195--222}, year={1997}, publisher={Elsevier}, doi={10.1016/S0012-365X(96)00365-2} } @article{athanasiadis1998noncrossing, title={On noncrossing and nonnesting partitions for classical reflection groups}, author={Athanasiadis, Christos A}, fjournal={The Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, volume={5}, number={1}, pages={R42}, year={1998}, doi={10.37236/1380} } @article {levear2020bijection, AUTHOR = {Levear, D.}, TITLE = {A bijection for {S}hi arrangement faces}, JOURNAL = {S\'{e}m. Lothar. Combin.}, FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire}, VOLUME = {82B}, YEAR = {2020}, PAGES = {Art. 47, 12}, MRCLASS = {52C35 (05A19)}, MRNUMBER = {4098268}, url = {https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2019/47.html} } @article{fishel2010bijection, title={A bijection between dominant Shi regions and core partitions}, author={Fishel, Susanna and Vazirani, Monica}, fjournal={European Journal of Combinatorics}, journal = {European J. Combin.}, volume={31}, number={8}, pages={2087--2101}, year={2010}, publisher={Elsevier}, doi={https://doi.org/10.1016/j.ejc.2010.05.014} } @article{tzanaki2015bijections, title={Bijections of dominant regions in the $ m $-Shi arrangements of type $ A $, $ B $ and $ C$}, author={Tzanaki, Eleni and Kallipoliti, Myrto}, journal={Discrete Mathematics \& Theoretical Computer Science}, year={2015}, publisher={Episciences. org}, url={https://dmtcs.episciences.org/2495/pdf} } @article{chapelier2020shi, title={Shi variety corresponding to an affine Weyl group}, author={Chapelier-Laget, Nathan}, journal={arXiv preprint arXiv:2010.04310}, year={2020} }