Definition 14.2.1. For any integer n\geq 1, and any 0\leq j \leq n we let \delta ^ n_ j : [n-1] \to [n] denote the injective order preserving map skipping j. For any integer n\geq 0, and any 0\leq j \leq n we denote \sigma ^ n_ j : [n + 1] \to [n] the surjective order preserving map with (\sigma ^ n_ j)^{-1}(\{ j\} ) = \{ j, j + 1\} .
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