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 A076269 Size of largest antichain in partition lattice Par(n). 3
 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 9, 10, 11, 14, 17, 20, 24, 29, 35, 40, 48, 55 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Par(n) is the set of partitions of n under "dominance order": partition P is <= partition Q iff the sum of the largest k parts of P is <= the corresponding sum for Q for all k. LINKS T. Brylawski, The lattice of integer partitions, Discrete Math. 6 (1973), 201-219. Edward Early, Chain Lengths in the Dominance Lattice, June 8, 2013; C. Greene and D. J. Kleitman, Longest Chains in the Lattice of Integer Partitions ordered by Majorization, Europ. J. Combinatorics 7 (1986), 1-10. FORMULA Order of growth is between n^(-5/2)e^(Pi*sqrt(2n/3)) and n^(-1)e^(Pi*sqrt(2n/3)). EXAMPLE a(10)=4; one antichain consists of 5+1+1+1+1+1, 4+3+1+1+1, 4+2+2+2 and 3+3+3+1. MATHEMATICA leq[p_, q_] := If[Length[p]

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)