# HG changeset patch
# User Anne Schilling <anne@math.ucdavis.edu>
# Date 1273025549 25200
# Node ID ffcf0730f20df1c2ae5196ad99385c4e4c6428b2
# Parent  963d81796bd31d4b8129842794ceb03a98c11431
Trac 8877: Implementation of methods to convert from k-bounded partitions to Grassmannian elements in the
affine Weyl group and the corresponding reduced word

diff --git a/sage/combinat/partition.py b/sage/combinat/partition.py
--- a/sage/combinat/partition.py
+++ b/sage/combinat/partition.py
@@ -1706,6 +1706,75 @@ class Partition_class(CombinatorialObjec
 
         return sage.combinat.skew_partition.SkewPartition([outer, inner])
 
+
+    def from_kbounded_to_reduced_word(p,k):
+	r"""
+	Maps a `k`-bounded partition to a reduced word for an element in 
+	the affine permutation group.
+
+        This uses the fact that there is a bijection between `k`-bounded partitions
+        and `(k+1)`-cores and an action of the affine nilCoxeter algebra of type
+        `A_k^{(1)}` on `(k+1)`-cores as described in [LM2006]_.
+
+        REFERENCES::
+
+            .. [LM2006] MR2167475 (2006j:05214)
+            L. Lapointe, J. Morse. Tableaux on `k+1`-cores, reduced words for affine permutations, and `k`-Schur expansions.
+            J. Combin. Theory Ser. A 112 (2005), no. 1, 44--81. 
+
+	EXAMPLES::
+
+	    sage: p=Partition([2,1,1])
+	    sage: p.from_kbounded_to_reduced_word(2)
+	    [2, 1, 2, 0]
+            sage: p=Partition([3,1])
+            sage: p.from_kbounded_to_reduced_word(3)
+            [3, 2, 1, 0]
+            sage: p.from_kbounded_to_reduced_word(2)
+            Traceback (most recent call last):
+            ...
+            ValueError: the partition must be 2-bounded
+            sage: p=Partition([])
+            sage: p.from_kbounded_to_reduced_word(2)
+            []
+	"""
+        p=p.k_skew(k)[0]
+        result = []
+        while p != []:
+	    corners = p.corners()
+	    c = p.content(corners[0][0],corners[0][1])%(k+1)
+	    result.append(Integer(c))
+	    list = [x for x in corners if p.content(x[0],x[1])%(k+1) ==c]
+	    for x in list:
+	        p = p.remove_cell(x[0])
+        return result
+
+    def from_kbounded_to_grassmannian(p,k):
+	r"""
+        Maps a `k`-bounded partition to a Grassmannian element in 
+	the affine Weyl group of type `A_k^{(1)}`.
+
+        For details, see the documentation of the method
+        :meth:`from_kbounded_to_reduced_word` .
+
+	EXAMPLES::
+
+            sage: p=Partition([2,1,1])
+	    sage: p.from_kbounded_to_grassmannian(2)
+	    [-1  1  1]
+	    [-2  2  1]
+	    [-2  1  2]
+            sage: p=Partition([])
+            sage: p.from_kbounded_to_grassmannian(2)
+            [1 0 0]
+            [0 1 0]
+            [0 0 1]
+	"""
+        from sage.combinat.root_system.weyl_group import WeylGroup
+        W=WeylGroup(['A',k,1])
+        return W.from_reduced_word(p.from_kbounded_to_reduced_word(k))
+
+
     def to_list(self):
         r"""
         Return self as a list.