Add references for paving matroids

Author: gmou3

src/doc/en/reference/references/index.rst

@@ -3689,6 +3689,9 @@ REFERENCES:
 .. [Ja1971] \N. Jacobson. *Exceptional Lie Algebras*. Marcel Dekker,
             Inc. New York. 1971. IBSN No. 0-8247-1326-5.
 
+.. [Jer2006] Mark Jerrum. *Two remarks concerning balanced matroids*.
+             Combinatorica 26, no. 6 (2006): 733-742.
+
 .. [Jet2008] \D. Jetchev. Global divisibility of Heegner points and
              Tamagawa numbers. Compos. Math. 144 (2008), no. 4, 811--826.
 
@@ -4991,6 +4994,10 @@ REFERENCES:
              *Yangians and classical Lie algebras*. (1994)
              :arxiv:`hep-th/9409025`
 
+.. [MNWW2011] Dillon Mayhew, Mike Newman, Dominic Welsh, and Geoff Whittle.
+              *On the asymptotic proportion of connected matroids*.
+              European Journal of Combinatorics. 2011 Aug 1;32(6):882-90.
+
 .. [Mol2007] Alexander Ivanovich Molev.
              *Yangians and Classical Lie Algebras*.
              Mathematical Surveys and Monographs.

src/sage/matroids/matroid.pyx

@@ -6210,6 +6210,10 @@ cdef class Matroid(SageObject):
             sage: M = matroids.Theta(4)
             sage: M.is_paving()
             False
+
+        REFERENCES:
+
+        [Oxl2011]_, p. 24.
         """
         if self.rank() >= 2:
             for _ in self.dependent_sets_iterator(self.rank() - 1):
@@ -6239,12 +6243,17 @@ cdef class Matroid(SageObject):
             sage: M.is_sparse_paving()
             False
 
+        REFERENCES:
+
+        The definition of sparse-paving matroids can be found in [MNWW2011]_.
+        The algorithm uses an alternative characterization from [Jer2006]_.
+
         TESTS::
 
             sage: M = matroids.Uniform(4, 50)  # fast because we don't check M.dual().is_paving()
             sage: M.is_sparse_paving()
             True
-            sage: for M in matroids.AllMatroids(8):
+            sage: for M in matroids.AllMatroids(8):  # optional - matroid_database
             ....:    assert M.is_sparse_paving() == (M.is_paving() and M.dual().is_paving())
         """
         if not self.is_paving():