## COMPUTATION OF P(14) THE NUMBER OF POSETS WITH 14 ELEMENTS : 1.338.193.159.771

### N. Lygeros and P. Zimmermann

For the history of this subject see records in combinatorics and number theory.
For the precise table of the computation of the number of posets with 12 or 13 elements see P(12) or P(13).

REFERENCES

• Calculs exhaustifs sur les posets d’au plus 7 éléments.
SINGULARITE, vol.2 n4 p.10-24, avril 1991. (N.Lygeros)
• Petits posets : dénombrement, représentabilité par cercles et compenseurs.
C.R.Acad.Sci.Paris, t.313, s.I, p.417-420, septembre 1991. (R.Fraïssé, N.Lygeros)
• The number of orders with thirteen elements.
Order, vol.9 p.203-204, 1992 (C.Chaunier, N.Lygeros)
• Le nombre de posets à isomorphie près ayant 12 éléments.
Theoretical Computer Science, n123 p.89-94, février 1994. (C.Chaunier, N.Lygeros)HELPERSRobert Erra, Bernard Landreau, John Lygeros, Jon Kierkegaard, Ilias Kotsireas, Thomas Papanikolaou, Robert Piche.PARTIAL RESULTS:

 Relations P(14,r) Name file r=0 1 – – r=1 1 – – r=2 3 – – r=3 7 – – r=4 19 – – r=5 47 – – r=6 133 – – r=7 355 – – r=8 1020 – – r=9 2921 – – r=10 8632 – – r=11 25486 – – r=12 75366 – – r=13 217990 – – r=14 613701 – – r=15 1659796 – – r=16 4290662 – – r=17 10541968 – – r=18 24574810 – – r=19 54282974 – – r=20 113695015 – – r=21 226043606 – – r=22 427434085 – – r=23 770364708 N. Lygeros – r=24 1326574992 P. Zimmermann – r=25 2187816296 Ilias Kotsireas – r=26 3463953205 Jon Kierkegaard res26 r=27 5276878418 Jon Kierkegaard res27 r=28 7750426625 Robert Erra, N. Lygeros res28 r=29 10995675430 P. Zimmermann – r=30 15093556839 Ilias Kotsireas, N. Lygeros res30 r=31 20075844431 Robert Piche, N. Lygeros res31 r=32 25908418088 Robert Piche – r=33 32478923331 Robert Piche – r=34 39592931224 Robert Piche – r=35 46979502004 Robert Piche res35 r=36 54307727007 N. Lygeros res36 r=37 61211924728 Bernard Landreau – r=38 67323642504 Thomas Papanikolaou res38 r=39 72305442194 Jon Kierkegaard, P. Zimmermann res39 r=40 75882802702 Jon Kierkegaard, P. Zimmermann res40 r=41 77869195951 Bernard Landreau res41 r=42 78181684187 Jon Kierkegaard, P. Zimmermann res42 r=43 76844939859 P. Zimmermann res43 r=44 73984081629 N. Lygeros res44 r=45 69807866652 Robert Piche, P. Zimmermann res45 r=46 64585100397 Jon Kierkegaard, N. Lygeros res46 r=47 58617924003 Jon Kierkegaard, P. Zimmermann res47 r=48 52215061893 N. Lygeros res48 r=49 45668403312 Bernard Landreau res49 r=50 39234427091 Jon Kierkegaard res50 r=51 33122134980 Jon Kierkegaard, N. Lygeros res51 r=52 27486947185 Jon Kierkegaard res52 r=53 22430638497 Jon Kierkegaard res53 r=54 18005406984 Jon Kierkegaard res54 r=55 14221396017 Jon Kierkegaard res55 r=56 11055548408 Jon Kierkegaard res56 r=57 8461181255 John Lygeros res57 r=58 6376703312 Robert Erra res58 r=59 4733381232 Jon Kierkegaard res59 r=60 3461298437 N. Lygeros – r=61 2493875402 – – r=62 1770675277 – – r=63 1239039207 – – r=64 854569812 – – r=65 580970065 – – r=66 389321463 – – r=67 257162269 – – r=68 167425100 – – r=69 107425128 – – r=70 67918114 – – r=71 42302121 – – r=72 25947267 – – r=73 15667333 – – r=74 9307819 – – r=75 5436986 – – r=76 3120222 – – r=77 1757459 – – r=78 970342 – – r=79 524242 – – r=80 276596 – – r=81 142020 – – r=82 70684 – – r=83 33907 – – r=84 15527 – – r=85 6724 – – r=86 2701 – – r=87 978 – – r=88 309 – – r=89 78 – – r=90 13 – – r=91 1 – –