OFFSET
0,3
COMMENTS
Axenovich's improvement to the Erdős strong Delta-system conjecture. Erdős and Rado called a family of sets {A1, A2, .., Ak} a strong Delta-system if all the intersections Ai INTERSECT Aj are identical, 1 <= i < j <= k. Denoting by f(n,k) the smallest integer m for which every family of n-sets {A1, A2, .., Am} contains k sets forming a strong Delta-system. Then Axenovich et al. proved f(n,3) < (n!)^((1/2) + epsilon)) < a(n) holds for every epsilon > 0, provided n is sufficiently large. - Jonathan Vos Post, Apr 29 2007; typos fixed by Li-yao Xia, May 06 2014
For n>0, a(n) is the least m>0 such that n! <= m^2. - Clark Kimberling, Jul 18 2012
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..807 (n = 0..300 from T. D. Noe)
M. Axenovich, D. Fon-Der-Flaass and A. Kostochka, On set systems without weak 3-Delta-subsystems, Discrete Math. 138(1995), 57-62.
Bela Bollobas, To Prove and Conjecture: Paul Erdős and His Mathematics, Am. Math. Monthly, 105 (March 1998)3, p. 232.
P. Erdős and R. Rado, Intersection theorems for systems of finite sets I, J. London Math. Soc. (2) 35(1960), 85-90.
P. Erdős and R. Rado, Intersection theorems for systems of finite sets II, J. London Math. Soc. (2) 44(1969), 467-479.
FORMULA
MAPLE
MATHEMATICA
Table[Ceiling[Sqrt[n!]], {n, 0, 30}] (* Wesley Ivan Hurt, May 06 2014 *)
PROG
(PARI) a(n) = ceil(sqrt(n!)) \\ Michel Marcus, Jul 30 2013
(Python)
from math import isqrt, factorial
def A055228(n): return 1+isqrt(factorial(n)-1) # Chai Wah Wu, Jul 28 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Jun 21 2000
EXTENSIONS
A comment stating that one of the terms was wrong has been deleted - the terms are correct. - T. D. Noe, Apr 22 2009
More terms from Wesley Ivan Hurt, May 06 2014
STATUS
approved