A note on a 2-enumeration of antisymmetric monotone triangles

TL;DR

This paper explains the connection between antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles, revealing a shared enumeration formula through a direct correspondence.

Contribution

It establishes a direct combinatorial correspondence that explains the shared enumeration formula for antisymmetric monotone triangles and quartered Aztec rectangle tilings.

Findings

The enumeration formula counts both structures.

A direct bijection between the two combinatorial objects.

Clarifies the combinatorial reason behind the shared formula.

Abstract

In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.