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Mesh patterns and the expansion of permutation statistics as sums of permutation patterns
[article]
2011
arXiv
pre-print
Any permutation statistic f:→ may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: f= Σ_τλ_f(τ)τ. 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=(π,R) is an occurrence of the permutation pattern π with additional restrictions specified by R on the relative position of the entries of the occurrence. We show
arXiv:1102.4226v2
fatcat:xgzbvobda5d4lpkgjz5geihuou