Doppelgangers: Bijections of Plane Partitions

被引：6

作者：

Hamaker, Zachary ^{[1
]}

Patrias, Rebecca ^{[2
]}

Pechenik, Oliver ^{[3
]}

Williams, Nathan ^{[4
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Quebec Montreal, LaCIM, Montreal, PQ H3C 3P8, Canada

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[4] Univ Texas Dallas, Dept Math Sci, Dallas, TX 75080 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2020年 / 2020卷 / 02期

基金：

美国国家科学基金会;

关键词：

SCHUBERT POLYNOMIALS; TABLEAUX; ELEMENTS; CHAINS; RULES; JEU;

D O I：

10.1093/imrn/rny018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We say two posets are doppelgangers if they have the same number of P-partitions of each height k. We give a uniform framework for bijective proofs that posets are doppelgangers by synthesizing K-theoretic Schubert calculus techniques of H. Thomas and A. Yong with M. Haiman's rectification bijection and an observation of R. Proctor. Geometrically, these bijections reflect the rational equivalence of certain subvarieties of minuscule flag manifolds. As a special case, we provide the 1st bijective proof of a 1983 theorem of R. Proctor-that plane partitions of height k in a rectangle are equinumerous with plane partitions of height k in a shifted trapezoid.

引用

页码：487 / 540

页数：54

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