Permutation classes of every growth rate above 2.48188
Mathematika, 56 (2010), 182–192.
We prove that there are permutation classes (hereditary properties of permutations) of every growth rate (Stanley-Wilf limit) at least λ≈2.48187, the unique real root of x5-2x4-2x2-2x-1, thereby establishing a conjecture of Albert and Linton.
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Related links:
- Steven Finch's short summary of growth rates.
- Michael Albert's FPSAC 2008 talk about growth rates.
- This work is briefly described in a talk I gave at the Rutgers Experimental Mathematics Seminar, and in a colloquium I gave at Dartmouth College.