Lozenge tilings of a hexagon with a horizontal intrusion

TL;DR

This paper derives explicit product formulas for counting lozenge tilings of a hexagon with a horizontal intrusion, connecting to plane partitions and analyzing asymptotic ratios.

Contribution

It provides new product formulas for lozenge tilings with intrusions and explores their asymptotic behavior, addressing a conjecture by Fulmek and Krattenthaler.

Findings

Derived explicit product formulas for tilings with intrusions.

Connected tiling counts to restricted plane partitions.

Analyzed asymptotic ratios of tiling counts.

Abstract

Motivated by a conjecture posed by Fulmek and Krattenthaler, we provide product formulas for the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion. As a direct corollary, we obtain a product formula for the number of boxed plane partitions with a certain restriction. We also investigate the asymptotic behavior of the ratio between the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion and that of a semiregular hexagon without an intrusion.