@article{d2a73aff2a264712a4a18b2f22c9cd77,
title = "Rhombic tilings and bott-samelson varieties",
abstract = "S. Elnitsky (1997) gave an elegant bijection between rhombic tilings of 2n-gons and commutation classes of reduced words in the symmetric group on n letters. P. Magyar (1998) found an important construction of the Bott-Samelson varieties introduced by H. C. Hansen (1973) and M. Demazure (1974). We explain a natural connection between S. Elnitsky{\textquoteright}s and P. Magyar{\textquoteright}s results. This suggests using tilings to encapsulate Bott-Samelson data (in type A). It also indicates a geometric perspective on S. Elnitsky{\textquoteright}s bijection. We also extend this construction by assigning desingularizations of Schubert varieties to the zonotopal tilings considered by B. Tenner (2006).",
author = "Laura Escobar and Oliver Pechenik and Tenner, {Bridget Eileen} and Alexander Yong",
note = "Received by the editors July 13, 2016, and, in revised form, July 6, 2017. 2010 Mathematics Subject Classification. Primary 05B45, 05E15, 14M15. The second author was supported by an NSF Graduate Research Fellowship. The third author was partially supported by a Simons Foundation Collaboration Mathematicians. The fourth author was supported by an NSF grant. The second author was supported by an NSF Graduate Research Fellowship. The third author was partially supported by a Simons Foundation Collaboration Grant for Mathematicians. We thank Allen Knutson and Alexander Woo for helpful comments. We are very grateful to an anonymous referee for comments that significantly improved the exposition of this paper.",
year = "2018",
month = jan,
day = "1",
doi = "10.1090/proc/13869",
language = "English (US)",
volume = "146",
pages = "1921--1935",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "5",
}