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Ladder

Generating functions — 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. A product of 3 polynomials, and what its coefficients count. The coefficients of a product of small polynomials, with the combinations of choices that reach one marked total written out beneath it.

    A polynomial that counts

    Hang a counting sequence on the powers of a variable and the two ways of combining choices — this and that, this or that — become multiplication and addition, so a recursion turns into an equation and the equation can be solved.

    rung 1 · discrete

All ladders