Posets, near unanimity functions and zigzags

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Abstract
With every poset we associate a class of coloured posets called zigzags. By means of zigzags we show that, if we delete a convex set from a finite lattice ordered set then the resulting poset has the strong selection property. We give the complete list of finite bounded irreducible posets admitting an n-ary near unanimity function, provided n ≤ 6. We present some examples and classes of posets with full descriptions of their zigzags.