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arXiv · 2609.19231

Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices

Yong Kong
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Abstract

Counting the number of coverings of $s$ dimers on two-dimensional quadratic lattices is considered as intractable and belongs to \#P-complete class. We reveal the structure of the exact solution to the problem and provide an explicit formula for it, which includes $s-1$ nesting sums. This results in an exponential time complexity of $O(2^s)$. The solution is explicitly determined by a sequence that exhibits double-exponential growth.

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Yong Kong. 2026-09-18. Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices. https://arxiv.org/abs/2609.19231

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