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arXiv · 2606.06513

An Alternative Proof of Dilworth's Theorem via Local Chain Merges

Tao Zhang
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Abstract

Several elegant proofs of Dilworth's theorem for finite posets already exist in the literature. In this note, we present an alternative inductive proof using a local legal merge lemma on chain ends. By combining this lemma with the bound established by Dilworth's theorem, we observe a direct consequence: every chain decomposition can be transformed into a minimal chain decomposition through a finite sequence of such legal merges

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Tao Zhang. 2026-05-31. An Alternative Proof of Dilworth's Theorem via Local Chain Merges. https://arxiv.org/abs/2606.06513

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