A bijective proof of the ASM theorem Part I: the operator formula

被引：9

作者：

Fischer, Ilse ^{[1
]}

Konvalinka, Matjaz ^{[2
,3
]}

机构：

[1] Univ Vienna, Fak Math, Vienna, Austria

[2] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[3] Inst Math Phys & Mech, Ljubljana, Slovenia

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2020年 / 27卷 / 03期

关键词：

ALTERNATING SIGN MATRICES; PLANE PARTITIONS; ENUMERATION;

D O I：

10.37236/9082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far. In this paper we provide the first bijective proof of the operator formula for monotone triangles, which has been the main tool for several non-combinatorial proofs of such equivalences. In this proof, signed sets and sijections (signed bijections) play a fundamental role.

引用

页码：1 / 29

页数：29

共 41 条

[1] PLANE PARTITIONS .5. THE TSSCPP CONJECTURE [J].