## COMPUTATION OF P(12) THE NUMBER OF POSETS WITH 12 ELEMENTS : 1.104.891.746

### C. Chaunier and N. Lygeros

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For the history of this subject you can see records in combinatorics and number theory.
For the precise table of the computation of the number of posets with
13 or 14 elements see P(13) or P(14).

REFERENCES

• Calculs exhaustifs sur les posets d’au plus 7 éléments.
SINGULARITE, vol.2 n4 p.10-24, 1991. (N.Lygeros)
Petits posets : dénombrement, représentabilité par cercles et compenseurs.
C.R.Acad.Sci.Paris, t.313, s.I, p.417-420, 1991. (R.Fraïssé, N.Lygeros)
• Progrès dans l’énumération des posets
C.R.Acad.Sci.Paris, t.314, s.I, p.691-694, 1992. (C.Chaunier, N.Lygeros)

 Relations P(12,r) r=0 1 r=1 1 r=2 3 r=3 7 r=4 19 r=5 47 r=6 133 r=7 352 r=8 997 r=9 2753 r=10 7558 r=11 19801 r=12 49795 r=13 117875 r=14 263019 r=15 550013 r=16 1080422 r=17 1993865 r=18 3469819 r=19 5707944 r=20 8909624 r=21 13234277 r=22 18766663 r=23 25468042 r=24 33157695 r=25 41495336 r=26 50008606 r=27 58130096 r=28 65270723 r=29 70888253 r=30 74562234 r=31 76042383 r=32 75275671 r=33 72402491 r=34 67726046 r=35 61666534 r=36 54699028 r=37 47302979 r=38 39908316 r=39 32869931 r=40 26443898 r=41 20792175 r=42 15984309 r=43 12020498 r=44 8844848 r=45 6370240 r=46 4491015 r=47 3100063 r=48 2094942 r=49 1386092 r=50 897535 r=51 568627 r=52 352196 r=53 213115 r=54 125818 r=55 72382 r=56 40515 r=57 21985 r=58 11545 r=59 5808 r=60 2779 r=61 1249 r=62 509 r=63 184 r=64 55 r=65 11 r=66 1

These results confirm R. Fraïssé’s conjecture on unimodality.