bisc_package.examples.known_classes package

Submodules

bisc_package.examples.known_classes.baxter_permutations module

Baxter permutations example.

Baxter permutations have applications in various areas of mathematics and are characterized by avoiding certain mesh patterns.

bisc_package.examples.known_classes.baxter_permutations.generate_baxter_approximation(max_length)

Generate an approximation of Baxter permutations using classical patterns.

Note: True Baxter permutations are defined by mesh patterns (2413, {(2,2)}) and (3142, {(2,2)}), but we use classical patterns as an approximation.

Parameters:

max_length (int) – Maximum length of permutations to generate

Return type:

List[Permutation]

Returns:

List of permutations avoiding classical patterns 2413 and 3142

bisc_package.examples.known_classes.baxter_permutations.demo_baxter_permutations()

Demonstrate the complexity of Baxter permutations.

bisc_package.examples.known_classes.corrected_baxter_test module

Corrected test for Baxter permutations. The issue was that I was using classical patterns, but Baxter permutations are defined by MESH patterns (2413, {(2,2)}) and (3142, {(2,2)}).

bisc_package.examples.known_classes.corrected_baxter_test.flatten(word)

Flatten a word to get relative order.

bisc_package.examples.known_classes.corrected_baxter_test.contains_pattern(permutation, pattern)

Check if permutation contains the classical pattern.

bisc_package.examples.known_classes.corrected_baxter_test.test_classical_vs_mesh_patterns()

Demonstrate the difference between classical and mesh patterns for Baxter permutations.

bisc_package.examples.known_classes.corrected_baxter_test.verify_known_baxter_sequences()

Verify against the known Baxter sequence.

bisc_package.examples.known_classes.corrected_baxter_test.demonstrate_mesh_pattern_concept()

Demonstrate what mesh patterns mean.

bisc_package.examples.known_classes.corrected_baxter_test.main()

Run the corrected Baxter analysis.

bisc_package.examples.known_classes.smooth_permutations module

Smooth permutations example.

Smooth permutations are related to smooth Schubert varieties in algebraic geometry. They are characterized by avoiding patterns 1324 and 2143.

bisc_package.examples.known_classes.smooth_permutations.generate_smooth_permutations(max_length)

Generate all smooth permutations up to max_length.

Parameters:

max_length (int) – Maximum length of permutations to generate

Return type:

List[Permutation]

Returns:

List of smooth permutations

bisc_package.examples.known_classes.smooth_permutations.demo_smooth_permutations()

Demonstrate BiSC on smooth permutations.

bisc_package.examples.known_classes.stack_sortable module

Stack-sortable permutations example.

Stack-sortable permutations are those that can be sorted using a single stack. They are characterized by avoiding the pattern 231.

bisc_package.examples.known_classes.stack_sortable.generate_stack_sortable(max_length)

Generate all stack-sortable permutations up to max_length.

Parameters:

max_length (int) – Maximum length of permutations to generate

Return type:

List[Permutation]

Returns:

List of stack-sortable permutations

bisc_package.examples.known_classes.stack_sortable.demo_stack_sortable()

Demonstrate BiSC on stack-sortable permutations.

bisc_package.examples.known_classes.test_baxter module

Test Baxter permutations example from the BiSC paper. According to the paper, Baxter permutations avoid the mesh patterns: (2413, {(2,2)}) and (3142, {(2,2)})

bisc_package.examples.known_classes.test_baxter.flatten(word)

Flatten a word to get relative order.

bisc_package.examples.known_classes.test_baxter.contains_pattern(permutation, pattern)

Check if permutation contains the classical pattern.

bisc_package.examples.known_classes.test_baxter.contains_mesh_pattern_simple(permutation, pattern, forbidden_regions)

Simplified mesh pattern containment check. This is a basic version - full mesh pattern checking is complex.

bisc_package.examples.known_classes.test_baxter.test_baxter_permutations()

Test Baxter permutations.

bisc_package.examples.known_classes.test_baxter.verify_known_baxter_examples()

Verify some specific known Baxter permutations.

Module contents

Examples for well-known permutation classes.