There are only finitely many $D(4)$-quintuples

There are only finitely many Diophantine quintuples

A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct elements increased by 1 is a perfect square. Diophantus found a set of four positive rationals with the above property. The first Diophantine quadruple was found by Fermat (the set {1, 3, 8, 120}). Baker and Davenport proved that this particular quadruple cannot be extended to a Diophantine quint...

Se p 20 09 There are only finitely many distance - regular graphs of fixed valency greater than two

There are only finitely many distance-regular graphs of fixed valency greater than two Abstract In this paper we prove the Bannai-Ito conjecture, namely that there are only finitely many distance-regular graphs of fixed valency greater than two.

Values of lambda and mu for which there are only finitely many feasible (v,k,lambda,mu)

There are finitely many Q-polynomial association schemes with given first multiplicity at least three

In this paper, we will prove a result which is formally dual to the long-standing conjecture of Bannai and Ito which claims that there are only finitely many distanceregular graphs of valency k for each k > 2. That is, we prove that, for any fixed m1 > 2, there are only finitely many cometric association schemes (X,R) with the property that the first idempotent in a Q-polynomial ordering has ra...

There are Finitely Many Triangle-Free Distance-Regular Graphs with Degree 8, 9 or 10

In this paper we prove that there are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10.