Asymptotics of principal evaluations of Schubert

Algebraic and Enumerative Combinatorics

30 January 09:00 - 09:50

Alejandro Morales - University of Massachusetts Amherst

Denote by u(n) the largest principal specialization of the Schubert polynomial of a permutation of size n. Stanley conjectured in 2017 that there is a limit $\lim_{n\to \infty} \log u(n)$ and asked for a limiting description of permutations achieving the maximum $u(n)$. Merzon and Smirnov had already conjectured in 2014 that this maximum is achieved on the class of layered permutations. We resolve both Stanley's problems restricted to layered permutations and give improvements on the bound of the possible value for the limit of $\log u(n)$. This is joint work with Igor Pak and Greta Panova.
Sara Billey
University of Washington
Petter Brändén
KTH Royal Institute of Technology
Sylvie Corteel
Université Paris Diderot, Paris 7
Svante Linusson
KTH Royal Institute of Technology


Svante Linusson


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