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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
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
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
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
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
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