Resolving Triple Systems into Regular Configurations A  lambdaTriple System(v), or a lambda xe2x80x93TS(V,calB), is a pair (V, calB) where V is a set and calB is a subset of the 3subsets of V so that every pair is in  exactly  lambda elements of calB. A regular configuration on p points with regularity rho on l blocks   is a pair (P,cal L) where calL is a collection of 3subsets of a (usually small) set P so that every p in P is in  exactly  rho elements of cal L, and cal Ll. The Pasch configuration (0,1,2,3,4,5, 012,035,245,134) has p6, l4, and rho2. A lambdaxe2x80x93TS(V,calB), is resolvable into a regular configuration Bbb C(P,cal L), or Bbb Cxe2x80x93resolvable, if  cal B can be partitioned into sets Pi_i so that for each i, (V,Pi_i) is isomorphic to a set of vertex disjoint copies of (P,cal L). If the configuration is a single block on three points this corresponds to ordinary resolvability of a Triple System.   In this paper we examine all regular configurations Bbb C on 6 or fewer blocks and construct Bbb Cxe2x80x93resolvable lambdaxe2x80x93Triple Systems of order v for many values of v and lambda. These conditions are also sufficient for each Bbb C having 4 blocks or fewer. For example for the Pasch configuration lambda equiv 0 pmod4 and v equiv 0 pmod6  are necessary and sufficient.

Using Algebraic Properties of Minimal Idempotents for Exhaustive Computer Generation of Association Schemes During the past few years we have obtained several new computer classification results on association schemes and in particular distance regular and strongly regular graphs. Central to our success is the use of two algebraic constraints based on properties of the minimal idempotents E_i of these association schemes : the fact that they are positive semidefinite and that they have known rank.   Incorporating these constraints into an actual isomorphfree exhaustive generation algorithm turns out to be somewhat complicated in practice. The main problem to be solved is that of numerical inaccuracy: we do not want to discard a potential solution because a value which is close to zero is misinterpreted as being negative (in the first case) or nonzero (in the second).   In this paper we give details on how this can be accomplished and also list some new classification results that have been recently obtained using this technique: the uniqueness of the strongly regular (126,50,13,24) graph and some new examples of antipodal distance regular graphs. We give an explicit description of a new antipodal distance regular 3cover of K_14, with vertices that can be represented as ordered triples of collinear points of the Fano plane.