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  • algorithms
    • alternating
      • alternating_crossings
      • is_alternating
      • is_face_alternating
    • canonical
    • closure
    • components_link
      • link_components
      • link_components_endpoints
      • number_of_link_components
    • connected_sum
    • cut_set
      • arc_cut_sets
      • cut_decomposition
      • cut_nodes
      • find_arc_cut_set
    • cycles
      • cycles
    • degree_sequence
      • degree_sequence
      • neighbour_sequence
    • disjoint_union
    • duality
      • arc_face_graph
      • dual_planar_diagram
    • join
      • bridge_join
      • crossing_join
    • naming
      • generate_node_names
      • multiple_unique_new_node_names
      • number_to_alpha
      • unique_new_node_name
    • orientation
      • all_orientations
      • orient
      • orient_edges
      • unorient
    • paths
      • bfs_shortest_path
      • path_from_endpoint
    • sanity
      • sanity_check
    • skein
      • crossing_to_vertex
      • smoothen_crossing
    • tangle
      • compose_tangles
      • is_integer_tangle
      • rotate
      • tangle_decompositions
    • tests
      • test_canonical
        • test_canonical
        • test_canonical_degenerate
        • test_canonical_degenerate_oriented
        • test_canonical_knots
        • test_canonical_knots_oriented
        • test_canonical_oriented
      • test_closure
        • test_closure
      • test_component_links
        • test_number_of_link_components
      • test_cut_set
        • test_arc_cut_set
        • test_cut_set_knotoid
        • test_cut_set_new
        • test_find_cut_sets
        • test_order_2
      • test_degree_sequence
        • test_deg_seq
      • test_disjoint_sum
        • test_disjoint_sum
        • test_unknots
      • test_features
        • test_bridges
      • test_orientation
        • test_orientation
      • test_skein
        • test_skein
      • test_sums
        • helper_test_connected_sum_on_knots
        • test_all_connected_sums
        • test_connected_sum
        • test_disjoint_sum
      • test_tangles
        • test_decompose
        • test_tangle_63
    • topology
      • bridges
      • edges
      • is_bridge
      • is_empty_diagram
      • is_kink
      • is_knot
      • is_knotoid
      • is_leaf
      • is_link
      • is_linkoid
      • is_loop
      • is_planar_graph
      • is_unknot
      • is_unlink
      • kink_region_iterator
      • kinks
      • leafs
      • loops
      • number_of_unknots
  • catalog
    • diagram_reader
    • diagram_writer
      • save_diagram_sets
      • save_diagrams
      • DiagramSetWriter
      • DiagramWriter
    • example
      • example_spatial_graph
      • handcuff_theta
      • oriented_trefoil
      • trefoil_knot
      • trefoil_theta
    • generate
      • generate_knot_diagrams
      • generate_simple_graphs
      • non_adjacent_combinations
    • graphs
      • bouquet
      • cycle_graph
      • handcuff_link
      • parallel_edges
      • path_graph
      • star_graph
      • theta_curve
      • wheel_graph
    • invariant_reader
      • load_invariant_table
    • invariant_writer
      • save_invariant_table
      • InvariantTableWriter
    • knot_tables
      • diagram_from_name
      • get_link_table
      • handcuff
      • knot
      • knot_invariants
      • knots
      • link
      • links
      • theta
      • thetas
    • tests
      • test_get_knot_by_names
        • test_get_knot_from_name
      • test_knot_table_invariants
        • compare_lazy_non_lazy
        • helper_lazy_load_diagram_table
        • helper_load_diagram_table
        • test_save_diagram_table
      • test_knots
        • test_get_knots
      • test_load_save_diagrams
        • test_read
        • test_read_write_diagram
        • test_read_write_diagram_sets
  • classes
    • convert
      • vertices_to_crossings
    • endpoint
      • Endpoint
      • IngoingEndpoint
      • OutgoingEndpoint
    • freezing
      • freeze
      • frozen
      • unfreeze
    • node
      • Node
    • planardiagram
      • planar_diagram_from_data
      • OrientedPlanarDiagram
      • PlanarDiagram
    • tests
      • test_endpoint
      • test_faces
        • test_faces
        • test_hopf
      • test_freezing
        • test_freeze
      • test_init
        • test_knot_name
      • test_nodes
        • test_remove_bivalent_vertex
    • views
      • ArcView
      • EndpointView
      • FaceView
      • FilteredNodeView
      • NodeView
  • drawing
    • circlepack
      • CirclePack
      • InvertAround
      • InvertPacking
      • NormalizePacking
      • acxyz
      • flower
      • place
      • testgrid
    • draw_matplotlib
      • average_color
      • canonically_rotate_layout
      • compute_PCA
      • draw
      • draw_from_layout
      • export_pdf
      • export_pdf_groups
      • export_png
      • get_style_from_style
      • to_color
      • Arrow
    • draw_tangle
      • add_corners_and_smoothen
      • angle_between_points
      • are_continuation
      • connect
      • crossings
      • draw
      • draw_smooth
      • integral
      • to_zigzag
      • TangleExpr
      • TangleProduct
      • TangleSum
      • ZigZag
    • dynamic_network
      • animate_simulation
      • plot_bead_frame
      • plot_force_history
      • plot_static_frame
      • simulation
      • Network
    • dynamic_simulation
      • init_network
    • icp
      • icp_complex
    • layout
      • bezier
      • circlepack_layout
    • tests
      • test_draw
        • test_draw_bonded
        • test_draw_bridges
        • test_draw_knot
        • test_draw_knotoid
        • test_draw_theta
        • test_thetas_sums
    • tutte_layout
      • tutte_layout
  • invariants
    • affine_index
      • affine_index_polynomial
    • alexander
      • alexander_polynomial
    • arrow
      • arrow_polynomial
      • disoriented_smoothing
    • bracket
      • bracket_polynomial
      • kauffman_bracket_skein_module
    • cache
      • Cache
    • homflypt
      • homflypt_polynomial
      • homflypt_polynomial_az
      • homflypt_polynomial_lm
      • homflypt_polynomial_vz
      • homflypt_polynomial_xyz
      • simplify_to_2_face
    • jones
      • jones_polynomial
    • kauffman
      • kauffman_polynomial
    • mock_alexander
      • mock_alexander_polynomial
    • module
      • Module
    • tests
      • test_homflypt
        • test_homflypt
      • test_jones
        • test_jones
      • test_tutte
        • test_deletion_contraction_cycle
        • test_deletion_contraction_parallel_edges
        • test_deletion_contraction_square_with_diagonal
      • test_yamada
        • test_thetas_recursive
        • test_yamada_examples_from_paper
        • test_yamada_moriuchi
        • test_yamada_reidemeister
    • tutte
      • deletion_contraction
      • tutte_polynomial
    • unplugging
    • writhe
    • yamada
      • yamada_polynomial
  • manipulation
    • attributes
      • clear_attributes
      • clear_diagram_attributes
      • clear_endpoint_attributes
      • clear_node_attributes
    • contract
      • contract_arc
    • insert
      • insert_arc
      • insert_arc2
      • insert_endpoint
      • insert_loop
      • insert_new_leaf
      • parallelize_arc
    • permute
      • permute_node
    • remove
      • remove_arc
      • remove_bivalent_vertex
      • remove_bivalent_vertices
      • remove_empty_nodes
      • remove_loops
      • remove_unknots
    • rewire
      • pull_and_plug_endpoint
      • replug_endpoint
      • swap_endpoints
    • subdivide
      • subdivide_arc
      • subdivide_arcs_around_node
      • subdivide_endpoint
      • subdivide_endpoint_by_crossing
    • symmetry
      • flip
      • mirror
    • tests
      • test_contract
        • test_contract_edge
        • test_contract_edge_attributes
      • test_insert
        • test_insert_attr
      • test_remove
        • test_remove_edge
  • notation
    • dispatcher
      • from_notation_dispatcher
      • to_notation_dispatcher
    • dt
      • from_dt_notation
      • to_dt_notation
    • em
      • from_condensed_em_notation
      • from_em_notation
      • to_condensed_em_notation
      • to_em_notation
    • native
      • from_knotpy_notation
      • to_knotpy_notation
    • pd
      • from_condensed_pd_notation
      • from_pd_notation
      • to_condensed_pd_notation
      • to_pd_notation
    • plantri
      • from_plantri_notation
      • to_plantri_notation
    • tests
      • test_notation
        • test_native_notation_from
        • test_native_notation_to
        • test_native_notation_to_from
      • test_plantri
        • test_from_plantri
  • reidemeister
    • choose_random_reidemeister_moves
    • detect_move_type
    • find_all_reidemeister_moves
    • make_all_reidemeister_moves
    • make_random_reidemeister_move
    • make_reidemeister_move
    • randomize_diagram
  • utils
    • algebra
      • laurent_polynomial_to_tuples
      • poly2str
      • reciprocal
      • str2poly
    • cache
      • Cache
    • chunked
    • combinatorics
      • combinations_with_limited_repetitions
      • iterable_depth
      • lexicographical_minimal_cyclic_rotation_shift
      • parted_permutations
      • union
    • decorators
      • total_ordering_from_compare
    • dict_utils
      • common_dict
      • compare_dicts
      • invert_dict
      • invert_dict_of_sets
      • invert_multi_dict
      • invert_nested_dict
      • ClassifierDict
      • JointDict
      • LazyEvalDict
      • LazyLoadDict
      • LazyLoadEvalDict
      • identitydict
    • disjoint_union_set
      • DisjointSetUnion
    • func_utils
      • min_elements_by
    • geometry
      • antipode
      • bisect
      • bisector
      • bounding_box
      • circle_through_points
      • inverse_point_through_circle
      • is_angle_between
      • middle
      • perpendicular_arc
      • perpendicular_arc_through_point
      • perpendicular_line
      • split
      • tangent_line
      • weighted_circle_center_mean
      • BoundingBox
      • Circle
      • CircularArc
      • Line
      • PolySegment
      • Segment
    • list_utils
      • flatten_nested_list
    • module
      • module
    • multiprogressbar
      • Bar
      • FakeBar
      • ProgressTracker
    • multiprogressbar2
      • Bar
      • FakeBar
      • ProgressBar
      • ProgressTracker
    • parsing
      • parse_arc
      • parse_arcs
      • parse_endpoint
      • parse_spaced_rows
      • universal_list_of_lists_parser
    • set_utils
      • powerset
      • LeveledSet
    • statistics
      • print_bar_chart
    • string_utils
      • multi_replace
      • nested_split
      • string_to_nested_tuple_with_prefixes
    • test
      • test_dict
        • test_dict
      • test_dsu
        • test_dsu
      • test_lazy_dict
        • test_lazy_eval
        • test_lazy_load
        • test_lazy_load_eval
      • test_module
        • test_module
      • test_parser
        • test_universal_list_of_lists_parser
      • test_set_utils
        • test_leveled_set
      • test_value_partitioner
        • mod2
        • mod3
        • test_value_partitioner
  • Reference
  • invariants
  • kauffman

kauffman#

The Kauffman 2-variable polynomial.

Functions

kauffman_polynomial(k)

© Copyright 2025, Boštjan Gabrovšek.

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