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Results tagged with nt.number-theory
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user 27829
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
45
votes
Accepted
Show that this ratio of factorials is always an integer
I found this paper
I. M. Gessel, G. Xin, A Combinatorial Interpretation of the
Numbers $6(2n!)/n!(n+2)!$, Journal of Integer Sequences 8 (2005) Article 05.2.3
whose abstract says:
It is well kno …
- 3,692
3
votes
Known results on cyclic difference sets
I'm not sure exactly what you mean because if you prove that there exists a cylcic $(v, k, \lambda)$-difference set for all $v$ except those that are excluded by known nonexistence results, you actual …
- 3,692
6
votes
Accepted
Is there an infinite number of combinatorial designs with $r=\lambda^{2}$
So I read your edit, and here's the answer: Yes. Infinitely many of them exist.
Anyway, if you only need a $2$-design with $r = \lambda^2$ which has at least one pair of blocks intersecting each othe …
- 3,692
6
votes
What is a random number? (poll experiment)
This isn't really an answer, but I couldn't post this in the comment field. So allow me to write this here.
There can't be a single definite answer to this question. But if you restrict your mathemat …
- 3,692
2
votes
Pairwise balanced designs with $r=\lambda^{2}$
Assuming you meant $r = \lambda^2$ (and also assuming you don't want repeated blocks), a proper approach might be to poke around the properties of $(r,\lambda)$-designs and their constructions to give …
- 3,692