Ticket #11410: trac_11410-zero_one_sequence_partitions-review-ts.patch

File trac_11410-zero_one_sequence_partitions-review-ts.patch, 3.3 KB (added by tscrim, 7 years ago)
  • sage/combinat/partition.py

    # 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 
    21r"""
    32Partitions
    43
    class Partition(CombinatorialObject, Ele 
    27192718
    27202719        The full `0-1` sequence is the sequence (infinite in both
    27212720        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 `0-1` 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 `0-1` sequence starts with infinitely many 0's and
    27272726        ends with infinitely many 1's.
    27282727
     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 24-25 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        **plus-minus diagrams**, **Comet code** [Sta1999]_, among others.
     2737
    27292738        OUTPUT:
    27302739
    27312740        The finite `0-1` sequence is obtained from the full `0-1`
    class Partition(CombinatorialObject, Ele 
    27332742        output sequence is finite, starts with a 1 and ends with a
    27342743        0 (unless it is empty, for the empty partition).
    27352744
     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
    27362751        EXAMPLES::
    27372752
    27382753            sage: Partition([5,4]).zero_one_sequence()
    class Partitions(UniqueRepresentation, P 
    41264141
    41274142    def from_zero_one(self, seq):
    41284143        r"""
    4129         Returns a partition from its `0-1` sequence.
     4144        Return a partition from its `0-1` sequence.
    41304145
    41314146        The full `0-1` 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 `0-1` 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 `0-1` 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()`
    41374158
    41384159        INPUT:
    41394160