Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
r""" Bijection classes for type `A_n^{(1)}`
Part of the (internal) classes which run the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin tableaux of type `A_n^{(1)}`.
AUTHORS:
- Travis Scrimshaw (2011-04-15): Initial version
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[5,2]])) sage: TestSuite(bijection).run() sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA sage: bijection = RCToKRTBijectionTypeA(RC(partition_list=[[],[],[],[]])) sage: TestSuite(bijection).run() """
#***************************************************************************** # Copyright (C) 2011, 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_n^{(1)}`. """
r""" Build the next state for type `A_n^{(1)}`.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[4,3]])) 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 first we subtract off for the n = max value (in the path) - 1, # then we remove 1 to match the indices between math and programming. # Always add a cell to the first singular value in the first # tableau we are updating. else:
# Insert a cell into the rightmost rigged partition
# Move to the left and update values as we have finished modifying # everything which affects its vacancy/partition values
# Update the final rigged tableau # Note if tabelauHeight = n+1, then we must have val = n+1 (in order # to be column strict increasing), but then tableau_height is never # greater than val, so we don't enter into this statement.
# Otherwise we just need to update the vacancy numbers that are affected
r""" Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type `A_n^{(1)}`. """
r""" Build the next state for type `A_n^{(1)}`.
EXAMPLES::
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA sage: bijection = RCToKRTBijectionTypeA(RC(partition_list=[[1],[1],[1],[1]])) sage: bijection.next_state(1) 5 """
# Calculate the rank and ell values
else:
# Determine the new rigged configuration by removing a box from the selected # string and then making the new string singular
|