trac #15431: Mention that we assume \lambda=1

Author: nathanncohen

src/sage/combinat/designs/bibd.py

@@ -47,6 +47,9 @@ def BalancedIncompleteBlockDesign(v,k,use_LJCR=False):
     distinct elements `x,y\in V` there is a unique element `S\in \mathcal C`
     such that `x,y\in S`.
 
+    More general definitions sometimes involve a `\lambda` parameter, and we
+    assume here that `\lambda=1`.
+
     For more information on BIBD, see the
     :wikipedia:`corresponding Wikipedia entry <Block_design#Definition_of_a_BIBD_.28or_2-design.29>`.
 

src/sage/combinat/designs/orthogonal_arrays.py

@@ -12,16 +12,19 @@ def transversal_design(k,n,check=True):
     r"""
     Return a transversal design of parameters `k,n`.
 
-    A transversal design of parameters `k, n` is a collection `\mathcal{S}`
-    of subsets of `V = V_1 \sqcup \cdots \sqcup V_k` (where each *group* `V_i`
-    has cardinality `n`) such that:
+    A transversal design of parameters `k, n` is a collection `\mathcal{S}` of
+    subsets of `V = V_1 \cup \cdots \cup V_k` (where the *groups* `V_i` are
+    disjoint and have cardinality `n`) such that:
 
     * Any `S \in \mathcal{S}` has cardinality `k` and intersects each group on
       exactly one element.
 
     * Any two elements from distincts groups are contained in exactly one
       element of `\mathcal{S}`.
 
+    More general definitions sometimes involve a `\lambda` parameter, and we
+    assume here that `\lambda=1`.
+
     For more information on transversal designs, see
     `<http://mathworld.wolfram.com/TransversalDesign.html>`_.
 
@@ -34,6 +37,11 @@ def transversal_design(k,n,check=True):
       guys), you may want to disable it whenever you want speed. Set to
       ``True`` by default.
 
+    .. NOTE::
+
+        This function returns transversal designs with
+        `V_1=\{0,\dots,n-1\},\dots,V_k=\{(k-1)n,\dots,kn-1\}`.
+
     .. SEEALSO::
 
         :func:`orthogonal_array` -- a tranversal design is an orthogonal array
@@ -150,8 +158,11 @@ def orthogonal_array(k,n,t=2,check=True):
 
     An orthogonal array of parameters `k,n,t` is a matrix with `k` columns
     filled with integers from `[n]` in such a way that for any `t` columns, each
-    of the `n^t` possible rows occurs exactly once. In particular, the matrix
-    has `n^t` rows.
+    of the `n^t` possible rows occurs exactly once. In
+    particular, the matrix has `n^t` rows.
+
+    More general definitions sometimes involve a `\lambda` parameter, and we
+    assume here that `\lambda=1`.
 
     For more information on orthogonal arrays, see
     :wikipedia:`Orthogonal_array`.