Indicators are boolean variables which record certain properties which a block design may have. We have included the following indicators:

`repeated_blocks`

True if the same set occurs more than once in the list of blocks.`resolvable`

True if the design has a*resolution*, which is a partition of the blocks into subsets called*parallel classes*or*resolution classes*, each of which forms a partition of the point set.`affine_resolvable`

True if the design is*affine resolvable*, which means that the design is resolvable and any two blocks not in the same parallel class of a resolution meet in a constant number of points. If the design is affine resolvable then we optionally give this constant (unless the design consists of a single parallel class, in which case is not defined).`equireplicate`

True if each point lies in a fixed number of blocks. If so, then we also optionally give the replication number .`constant_blocksize`

True if each block contains a fixed number of points. If so, then we optionally also give the block size .`t_design`

True if the block design is a*t*-design for some . This means that the design has constant block size and that any points are contained in a positive constant number of blocks. If so, then we optionally give the maximum value of for which this holds.`connected`

True if the incidence graph of the block design is a connected graph. (The*incidence graph*or*Levi graph*of a block design is the bipartite graph whose vertices are the points and blocks of the design, a point and block being adjacent if the point is contained in the block.) We optionally give the number of connected components of the incidence graph.`pairwise_balanced`

True if and the number of blocks containing two distinct points is a positive constant . If so, then we optionally give this .`variance_balanced`

True if and the intra-block information matrix has identical, nonzero eigenvalues. Equivalently, the canonical variances are all equal (and finite). For definitions of terms used here, see section 7.6 on Statistical Properties.`efficiency_balanced`

True if and the statistical canonical efficiency factors are identical and nonzero. For equireplicate designs, this is equivalent to variance_balanced, but not genenerally otherwise. Also see the section 7.6 Statistical Properties.`cyclic`

True if the design has an automorphism which permutes all the points in a single cycle.`one_rotational`

True if the design has an automorphism which fixes one point and permutes the other points in a single cycle.

In the last two cases, an automorphism with the stated properties can be
found under `cycle_type_representatives`, described in
section 7.4 on Automorphisms.

The several different sorts of balance are explained in the http://designtheory.org/library/encycEncyclopaedia. For a (binary) design with constant block size, variance balance reduces to pairwise balance. For a equireplicate (binary) design with constant block size, efficiency balance reduces to pairwise balance.

The indicators for our example are:

<indicators> <repeated_blocks flag="false"> </repeated_blocks> <resolvable flag="false"> </resolvable> <affine_resolvable flag="false"> </affine_resolvable> <equireplicate flag="true" r="3"> </equireplicate> <constant_blocksize flag="true" k="3"> </constant_blocksize> <t_design flag="true" maximum_t="2"> </t_design> <connected flag="true" no_components="1"> </connected> <pairwise_balanced flag="true" lambda="1"> </pairwise_balanced> <variance_balanced flag="true"> </variance_balanced> <efficiency_balanced flag="true"> </efficiency_balanced> <cyclic flag="true"> </cyclic> <one_rotational flag="false"> </one_rotational> </indicators>