A Bijective Proof of the ASM Theorem Part II: ASM Enumeration and ASM-DPP Relation

被引：2

作者：

Fischer, Ilse ^{[1
]}

Konvalinka, Matjaz ^{[2
,3
]}

机构：

[1] Univ Vienna, A-1090 Vienna, Austria

[2] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

[3] Inst Math Phys & Mech, Ljubljana 1000, Slovenia

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 10期

基金：

奥地利科学基金会;

关键词：

DETERMINANTS;

D O I：

10.1093/imrn/rnaa304

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is the 2nd in a series of planned papers that provide 1st bijective proofs of alternating sign matrix (ASM) results. Based on the main result from the 1st paper, we construct a bijective proof of the enumeration formula for ASMs and of the fact that ASMs are equinumerous with descending plane partitions. We are also able to refine these bijections by including the position of the unique 1 in the top row of the matrix. Our constructions rely on signed sets and related notions. The starting point for these constructions were known "computational" proofs, but the combinatorial point of view led to several drastic modifications. We also provide computer code where all of our constructions have been implemented.

引用

页码：7203 / 7230

页数：28

共 16 条

[1] PLANE PARTITIONS(III) - WEAK MACDONALD CONJECTURE [J].