# HG changeset patch
# User Travis Scrimshaw
# Date 1361735058 28800
# Node ID 0ba09912016ce1c7cc2c0045d5302bd9fc553ed4
# Parent 14c77d0c4ba1606fe9cf822add066825dcf056f6
Review patch for #11410.
diff git a/sage/combinat/partition.py b/sage/combinat/partition.py
 a/sage/combinat/partition.py
+++ b/sage/combinat/partition.py
@@ 1,4 +1,3 @@

r"""
Partitions
@@ 2719,13 +2718,23 @@ class Partition(CombinatorialObject, Ele
The full `01` sequence is the sequence (infinite in both
directions) indicating the steps taken when following the
 outer rim of the diagram of the partition. In the English
 notation, a 1 corresponds to an East step, while a 0
 corresponds to a North step.

 Every full `01` sequence starts with infinitely many 0's and
+ outer rim of the diagram of the partition. We use the convention
+ that in English convention, a 1 corresponds to an East step, and
+ a 0 corresponds to a North step.
+
+ Note that every full `01` sequence starts with infinitely many 0's and
ends with infinitely many 1's.
+ One place where these arise is in the affine symmetric group where
+ one takes an affine permutation `w` and every `i` such that
+ `w(i) \leq 0` corresponds to a 1 and `w(i) > 0` corresponds to a 0.
+ See pages 2425 of [LLMMSZ13]_ for connections to affine Grassmannian
+ elements (note there they use the French convention for their
+ partitions).
+
+ These are also known as **path sequences**, **Maya diagrams**,
+ **plusminus diagrams**, **Comet code** [Sta1999]_, among others.
+
OUTPUT:
The finite `01` sequence is obtained from the full `01`
@@ 2733,6 +2742,12 @@ class Partition(CombinatorialObject, Ele
output sequence is finite, starts with a 1 and ends with a
0 (unless it is empty, for the empty partition).
+ REFERENCES:
+
+ .. [LLMMSZ13] Thomas Lam, Luc Laponte, Jennifer Morse, Anne Schilling,
+ Mark Shimozono, and Mike Zabrocki. `k`Schur Functions and Affine
+ Schubert Calculus. 2013. :arxiv:`1301.3569`.
+
EXAMPLES::
sage: Partition([5,4]).zero_one_sequence()
@@ 4126,14 +4141,20 @@ class Partitions(UniqueRepresentation, P
def from_zero_one(self, seq):
r"""
 Returns a partition from its `01` sequence.
+ Return a partition from its `01` sequence.
The full `01` sequence is the sequence (infinite in both
 directions) indicating the steps taken when following the outer
 rim of the diagram of the partition. In the English notation, a 1
 corresponds to an East step, while a 0 corresponds to a North
 step. Every `01` sequence starts with infinitely many 0's and ends
 with infinitely many 1's.
+ directions) indicating the steps taken when following the
+ outer rim of the diagram of the partition. We use the convention
+ that in English convention, a 1 corresponds to an East step, and
+ a 0 corresponds to a North step.
+
+ Note that every full `01` sequence starts with infinitely many 0's and
+ ends with infinitely many 1's.
+
+ .. SEEALSO::
+
+ :meth:`Partition.zero_one_sequence()`
INPUT: