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Ladder

Posets — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. The widest layer of the subsets of a set of 4. A Hasse diagram of a small order with the widest layer marked, and the largest set of mutually incomparable elements found by examining every subset.

    The widest layer and the longest chain

    Order sixteen subsets by inclusion and ask for the largest collection with no two comparable. The answer is the six subsets of size two — the widest layer — and no cleverer collection beats it. Ask instead for the fewest chains covering everything, and the answer is the same number again.

    rung 1 · discrete

All ladders