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Mesh Patterns and the Expansion of Permutation Statistics as Sums of Permutation Patterns
2011
Electronic Journal of Combinatorics
Any permutation statistic $f:{\mathfrak{S}}\to{\mathbb C}$ may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: $f= \Sigma_\tau\lambda_f(\tau)\tau$. To provide explicit expansions for certain statistics, we introduce a new type of permutation patterns that we call mesh patterns. Intuitively, an occurrence of the mesh pattern $p=(\pi,R)$ is an occurrence of the permutation pattern $\pi$ with additional restrictions specified by $R$ on the
doi:10.37236/2001
fatcat:skswqrflhfeadmt36wp4crlvse