# 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
diff --git a/sage/combinat/partition.py b/sage/combinat/partition.py
 a r""" Partitions class Partition(CombinatorialObject, Ele The full 0-1 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 0-1 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 0-1 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 24-25 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**, **plus-minus diagrams**, **Comet code** [Sta1999]_, among others. OUTPUT: The finite 0-1 sequence is obtained from the full 0-1 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() class Partitions(UniqueRepresentation, P def from_zero_one(self, seq): r""" Returns a partition from its 0-1 sequence. Return a partition from its 0-1 sequence. The full 0-1 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 0-1 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 0-1 sequence starts with infinitely many 0's and ends with infinitely many 1's. .. SEEALSO:: :meth:Partition.zero_one_sequence() INPUT: