Abstract
A classical result of Erd\H os, Lov\'asz and Spencer from the late 1970s asserts that the dimension of the feasible region of homomorphic densities of graphs with at most $k$ vertices in large graphs is equal to the number of connected graphs with at most $k$ vertices. Glebov et al. showed that pattern densities of indecomposable permutations are independent, i.e., the dimension of the feasible region of densities of $k$-patterns is at least the number of non-trivial indecomposable permutations of size at most $k$. We identify a larger set of permutations, which are called Lyndon permutations, whose pattern densities are independent, and show that the dimension of the feasible region of densities of $k$-patterns is equal to the number of non-trivial Lyndon permutations of size at most $k$.
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