Some Statistics on the Hypercubes of Catalan Permutations
نویسنده
چکیده
For a permutation σ of length 3, we define the oriented graph Qn(σ). The graph Qn(σ) is obtained by imposing edge constraints on the classical oriented hypercube Qn, such that each path going from 0 to 1 in Qn(σ) bijectively encodes a permutation of size n avoiding the pattern σ. The orientation of the edges in Qn(σ) naturally induces an order relation σ among its nodes. First, we characterize σ. Next, we study several enumerative statistics on Qn(σ), including the number of intervals, the number of intervals of fixed length k, and the number of paths (or permutations) intersecting a given node.
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