Skew doubled shifted plane partitions: Calculus and asymptotics

Guo-Niu Han; Huan Xiong; Guo-Niu Han; Huan Xiong

doi:10.3934/era.2020094

Electronic Research Archive

2021, Volume 29, Issue 1: 1841-1857. doi: 10.3934/era.2020094

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Skew doubled shifted plane partitions: Calculus and asymptotics

Guo-Niu Han ,
Huan Xiong ^,

Université de Strasbourg, CNRS, IRMA UMR 7501, F-67000 Strasbourg, France

Received: 01 April 2020 Revised: 01 July 2020 Published: 16 September 2020
Primary: 05A16, 05A17, 05E05

In this paper, we establish a new summation formula for Schur processes, called the complete summation formula. As an application, we obtain the generating function and the asymptotic formula for the number of doubled shifted plane partitions, which can be viewed as plane partitions "shifted at the two sides". We prove that the order of the asymptotic formula depends only on the diagonal width of the doubled shifted plane partition, not on the profile (the skew zone) itself. By using similar methods, the generating function and the asymptotic formula for the number of symmetric cylindric partitions are also derived.
- Plane partition,
- cylindric partition,
- Schur process,
- asymptotic formula
Citation: Guo-Niu Han, Huan Xiong. Skew doubled shifted plane partitions: Calculus and asymptotics[J]. Electronic Research Archive, 2021, 29(1): 1841-1857. doi: 10.3934/era.2020094

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Abstract

In this paper, we establish a new summation formula for Schur processes, called the complete summation formula. As an application, we obtain the generating function and the asymptotic formula for the number of doubled shifted plane partitions, which can be viewed as plane partitions "shifted at the two sides". We prove that the order of the asymptotic formula depends only on the diagonal width of the doubled shifted plane partition, not on the profile (the skew zone) itself. By using similar methods, the generating function and the asymptotic formula for the number of symmetric cylindric partitions are also derived.

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