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r""" Bijection classes for type `A_{2n-1}^{(2)}`.
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type `A_{2n-1}^{(2)}`.
AUTHORS:
- Travis Scrimshaw (2012-12-21): Initial version
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd sage: bijection = KRTToRCBijectionTypeA2Odd(KRT(pathlist=[[-1,2]])) sage: TestSuite(bijection).run() sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[],[],[]])) sage: TestSuite(bijection).run() """
#***************************************************************************** # Copyright (C) 2012 Travis Scrimshaw <tscrim@ucdavis.edu> # # Distributed under the terms of the GNU General Public License (GPL) # # This code is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # The full text of the GPL is available at: # # http://www.gnu.org/licenses/ #*****************************************************************************
r""" Specific implementation of the bijection from KR tableaux to rigged configurations for type `A_{2n-1}^{(2)}`.
This inherits from type `A_n^{(1)}` because we use the same methods in some places. """
r""" Build the next state for type `A_{2n-1}^{(2)}`.
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd sage: bijection = KRTToRCBijectionTypeA2Odd(KRT(pathlist=[[-2,3]])) sage: bijection.cur_path.insert(0, []) sage: bijection.cur_dims.insert(0, [0, 1]) sage: bijection.cur_path[0].insert(0, [3]) sage: bijection.next_state(3) """ # Note that we must subtract 1 from n to match the indices.
# If it is a regular value, we follow the A_n rules
# Always add a cell to the first singular value in the first # tableau we are updating. else:
# Add cells similar to type A_n but we move to the right until we # reach the value of n
# Now go back following the regular A_n rules
# Update the final rigged partitions
r""" Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type `A_{2n-1}^{(2)}`. """
r""" Build the next state for type `A_{2n-1}^{(2)}`.
TESTS::
sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[1],[2,1],[2]])) sage: bijection.next_state(1) -2 """
# Calculate the rank and ell values
else:
# Now go back # Modified form of _find_singular_string() self.cur_partitions[a].vacancy_numbers[i] == self.cur_partitions[a].rigging[i]:
else:
# Determine the new rigged configuration by removing a box from the selected # string and then making the new string singular
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