A lower bound on forcing numbers based on height functions

TL;DR

This paper introduces a polynomial-time computable lower bound on the forcing numbers of domino tilings, which is sharp for certain square regions and potentially useful for analyzing tiling configurations.

Contribution

It provides a new, efficiently computable lower bound on forcing numbers based on height functions, improving understanding of domino tilings.

Findings

Lower bound is sharp for 2n by 2n squares.

Lower bound is applicable to various cases.

Bound can be computed in polynomial time.

Abstract

We establish a lower bound on the forcing numbers of domino tilings computable in polynomial time based on height functions. This lower bound is sharp for a 2n by 2n square as well as other cases.