A 2-chain can interlock with an open 10-chain

TL;DR

This paper proves that a 2-chain can interlock with an open 10-chain, improving previous results and suggesting that 10 is likely the minimal chain length needed for such interlocking.

Contribution

The paper demonstrates that a 2-chain can interlock with an open 10-chain, advancing the known minimal chain length for interlocking from 11 to 10.

Findings

Interlocking between a 2-chain and a 10-chain is established.

Previous minimal interlocking chain length was 11, now improved to 10.

Arguments suggest that 10 is likely the minimal chain length for interlocking.

Abstract

It is an open problem, posed in \cite{SoCG}, to determine the minimal $k$ such that an open flexible $k$-chain can interlock with a flexible 2-chain. It was first established in \cite{GLOSZ} that there is an open 16-chain in a trapezoid frame that achieves interlocking. This was subsequently improved in \cite{GLOZ} to establish interlocking between a 2-chain and an open 11-chain. Here we improve that result once more, establishing interlocking between a 2-chain and a 10-chain. We present arguments that indicate that 10 is likely the minimum.