# HG changeset patch
# User Travis Scrimshaw <tscrim@ucdavis.edu>
# 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

b


1   
2  1  r""" 
3  2  Partitions 
4  3  
… 
… 
class Partition(CombinatorialObject, Ele 
2719  2718  
2720  2719  The full `01` sequence is the sequence (infinite in both 
2721  2720  directions) indicating the steps taken when following the 
2722   outer rim of the diagram of the partition. In the English 
2723   notation, a 1 corresponds to an East step, while a 0 
2724   corresponds to a North step. 
2725   
2726   Every full `01` sequence starts with infinitely many 0's and 
 2721  outer rim of the diagram of the partition. We use the convention 
 2722  that in English convention, a 1 corresponds to an East step, and 
 2723  a 0 corresponds to a North step. 
 2724  
 2725  Note that every full `01` sequence starts with infinitely many 0's and 
2727  2726  ends with infinitely many 1's. 
2728  2727  
 2728  One place where these arise is in the affine symmetric group where 
 2729  one takes an affine permutation `w` and every `i` such that 
 2730  `w(i) \leq 0` corresponds to a 1 and `w(i) > 0` corresponds to a 0. 
 2731  See pages 2425 of [LLMMSZ13]_ for connections to affine Grassmannian 
 2732  elements (note there they use the French convention for their 
 2733  partitions). 
 2734  
 2735  These are also known as **path sequences**, **Maya diagrams**, 
 2736  **plusminus diagrams**, **Comet code** [Sta1999]_, among others. 
 2737  
2729  2738  OUTPUT: 
2730  2739  
2731  2740  The finite `01` sequence is obtained from the full `01` 
… 
… 
class Partition(CombinatorialObject, Ele 
2733  2742  output sequence is finite, starts with a 1 and ends with a 
2734  2743  0 (unless it is empty, for the empty partition). 
2735  2744  
 2745  REFERENCES: 
 2746  
 2747  .. [LLMMSZ13] Thomas Lam, Luc Laponte, Jennifer Morse, Anne Schilling, 
 2748  Mark Shimozono, and Mike Zabrocki. `k`Schur Functions and Affine 
 2749  Schubert Calculus. 2013. :arxiv:`1301.3569`. 
 2750  
2736  2751  EXAMPLES:: 
2737  2752  
2738  2753  sage: Partition([5,4]).zero_one_sequence() 
… 
… 
class Partitions(UniqueRepresentation, P 
4126  4141  
4127  4142  def from_zero_one(self, seq): 
4128  4143  r""" 
4129   Returns a partition from its `01` sequence. 
 4144  Return a partition from its `01` sequence. 
4130  4145  
4131  4146  The full `01` sequence is the sequence (infinite in both 
4132   directions) indicating the steps taken when following the outer 
4133   rim of the diagram of the partition. In the English notation, a 1 
4134   corresponds to an East step, while a 0 corresponds to a North 
4135   step. Every `01` sequence starts with infinitely many 0's and ends 
4136   with infinitely many 1's. 
 4147  directions) indicating the steps taken when following the 
 4148  outer rim of the diagram of the partition. We use the convention 
 4149  that in English convention, a 1 corresponds to an East step, and 
 4150  a 0 corresponds to a North step. 
 4151  
 4152  Note that every full `01` sequence starts with infinitely many 0's and 
 4153  ends with infinitely many 1's. 
 4154  
 4155  .. SEEALSO:: 
 4156  
 4157  :meth:`Partition.zero_one_sequence()` 
4137  4158  
4138  4159  INPUT: 
4139  4160  