Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Asymptotics of principal evaluations of Schubert polynomials for layered permutations


Authors: Alejandro H. Morales, Igor Pak and Greta Panova
Journal: Proc. Amer. Math. Soc. 147 (2019), 1377-1389
MSC (2010): Primary 05A05, 05A16, 05E05, 14N15
DOI: https://doi.org/10.1090/proc/14369
Published electronically: January 9, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Denote by $ u(n)$ the largest principal specialization of the Schubert polynomial

$\displaystyle u(n) \, := \, \max _{w \in S_n} \hskip .06cm \mathfrak{S}_w(1,\ldots ,1).$    

Stanley conjectured that there is a limit

$\displaystyle \lim _{n\to \infty } \, \frac {1}{n^2} \hskip .06cm \log u(n),$    

and asked for a limiting description of permutations achieving the maximum $ u(n)$. Merzon and Smirnov conjectured in [Eur. J. Math. 2 (2016), pp. 227-245] that this maximum is achieved on layered permutations. We resolve both of Stanley's problems restricted to layered permutations.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05A05, 05A16, 05E05, 14N15

Retrieve articles in all journals with MSC (2010): 05A05, 05A16, 05E05, 14N15


Additional Information

Alejandro H. Morales
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
Email: ahmorales@math.umass.edu

Igor Pak
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095
Email: pak@math.ucla.edu

Greta Panova
Affiliation: Institute of Advanced Studies, Princeton, New Jersey 08540 –and– Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Address at time of publication: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: gpanova@usc.edu

DOI: https://doi.org/10.1090/proc/14369
Received by editor(s): May 29, 2018
Received by editor(s) in revised form: June 27, 2018
Published electronically: January 9, 2019
Additional Notes: The second and third authors were partially supported by the NSF
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2019 American Mathematical Society