combin · Tableau¶

9 accepted declarations. Python and Rust forms, contracts, evidence, failure boundaries, and checked usages are kept together below.

Worked example¶

The complete checked program Weight characters and second Chern classes for polynomial GL representations uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Weight characters and second Chern classes for polynomial GL representations."""

from noether.combin import Partition, Tableau
from noether.groups import PolynomialGlRepresentation

shape = Partition((2, 1))
tableaux = Tableau.semistandard(shape, 3)
assert tableaux.cardinality == 8
assert next(tableaux).content(3) == (2, 1, 0)

wedge_two = PolynomialGlRepresentation(4, Partition((1, 1)))
assert wedge_two.weyl_dimension == 6
assert wedge_two.descends_to_sl_quotient(2)
assert wedge_two.second_chern_index() == 2
assert wedge_two.second_chern_index_from_weights() == 2

example = PolynomialGlRepresentation(6, shape)
assert example.weyl_dimension == 70
assert example.second_chern_index() == 33
example.verify_second_chern_index()

character = example.sl_character()
assert character.dimension == 70
assert character.chern_class(2).nonzero_term_count > 0

print("tableaux=8; c2(wedge^2 gamma_4)=2c2; c2(gamma_6^(2,1))=33c2")

Run it with .venv/bin/python examples/27_weight_characters.py.

`combin.Tableau`¶

A thin Python handle around Noether's semistandard integer tableau.

PythonRust

Tableau(rows: Sequence[Sequence[int]])

noether::combin::Tableau · Direct Rust declaration

pub struct Tableau { /* private fields */ }

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: examples/27_weight_characters.py:5 · examples/27_weight_characters.py:9 · validation/unit/combin/test_acceptance_workload.py:18 · validation/unit/combin/test_acceptance_workload.py:35 · validation/unit/combinatorics/test_tableau_rsk.py:12 · validation/unit/combinatorics/test_tableau_rsk.py:14

`combin.Tableau.eq`¶

Test mathematical equality with another value.

PythonRust

(self, other: object) -> bool

noether::combin::Tableau · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

`combin.Tableau.content`¶

Content vector in the positive alphabet 1..=alphabet_size.

Detailed contract

Content in the positive alphabet 1..=alphabet_size. The returned arbitrary-precision count at position i is the number of entries equal to i + 1. A tableau whose entries do not belong to the requested alphabet is rejected rather than silently truncated.

PythonRust

(self, alphabet_size: int) -> tuple[int, ...]

noether::combin::Tableau::content · Direct Rust declaration

pub fn content(&self, alphabet_size: usize) -> Result<Vec<Integer>, CombinError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: examples/27_weight_characters.py:11 · validation/unit/groups/test_weight_characters.py:30 · validation/unit/infra/test_docs_site_generator.py:180 · validation/unit/infra/test_release_candidate.py:86 · validation/unit/infra/test_wheel_sbom.py:98 · validation/parity/m1_bsgs.py:65

`combin.Tableau.from_json`¶

Deserialize and revalidate shape, rows, and columns.

PythonRust

(value: str) -> Tableau

noether::combin::Tableau · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106 · validation/unit/combin/test_graph_facade.py:25 · validation/unit/combinatorics/test_kashiwara_crystal.py:32

`combin.Tableau.rows`¶

Immutable row-major entries as Python integers.

Detailed contract

Row-major entries.

PythonRust

(self) -> tuple[tuple[int, ...], ...]

noether::combin::Tableau::rows · Direct Rust declaration

pub fn rows(&self) -> &[Vec<Integer>]

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: examples/distributed/f2_linear_algebra.py:56 · validation/unit/combin/test_acceptance_workload.py:36 · validation/unit/combin/test_acceptance_workload.py:37 · validation/unit/combinatorics/test_tableau_rsk.py:15 · validation/unit/combinatorics/test_tableau_rsk.py:42 · validation/unit/combinatorics/test_tableau_rsk.py:43

`combin.Tableau.rsk`¶

Robinson--Schensted--Knuth row insertion for an integer word.

Detailed contract

Robinson–Schensted–Knuth row insertion for an integer word. Returns the semistandard insertion tableau and standard recording tableau. The typed failure is only the explicit Young-diagram bound.

PythonRust

(word: Sequence[int]) -> tuple[Tableau, Tableau]

noether::combin::Tableau::rsk · Direct Rust declaration

pub fn rsk(word: &[Integer]) -> Result<(Self, Self), CombinError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: validation/unit/combin/test_acceptance_workload.py:35 · validation/unit/combinatorics/test_tableau_rsk.py:40 · validation/unit/combinatorics/test_tableau_rsk.py:49 · validation/parity/combinatorics/test_tableau_rsk_parity.py:59

`combin.Tableau.semistandard`¶

Lazily enumerate semistandard tableaux of one shape and alphabet.

Detailed contract

Lazily enumerate semistandard tableaux of shape in row-major lexicographic order over the alphabet 1..=maximum_entry.

PythonRust

(shape: Partition, maximum_entry: int) -> SemistandardTableaux

noether::combin::Tableau::semistandard · Direct Rust declaration

pub fn semistandard( shape: Partition, maximum_entry: usize, ) -> Result<SemistandardTableaux, CombinError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: examples/27_weight_characters.py:9 · validation/unit/combinatorics/test_tableau_rsk.py:3 · validation/unit/groups/test_weight_characters.py:20 · validation/corpus/groups/gelfand-tsetlin-weight-character.py:11 · validation/corpus/groups/gelfand-tsetlin-weight-character.py:3

`combin.Tableau.shape`¶

Canonical partition shape.

Detailed contract

Young-diagram shape derived from the rows.

PythonRust

(self) -> Partition

noether::combin::Tableau::shape · Direct Rust declaration

pub const fn shape(&self) -> &Partition

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: examples/27_weight_characters.py:19 · examples/27_weight_characters.py:8 · examples/27_weight_characters.py:9 · examples/distributed/f2_linear_algebra.py:51 · examples/distributed/f2_linear_algebra.py:52 · validation/unit/combin/test_acceptance_workload.py:38

`combin.Tableau.to_json`¶

Serialize canonical row data; arbitrary-precision entries use decimal strings.

PythonRust

(self) -> str

noether::combin::Tableau · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, graph-core, perm-core
GIL	attached / bounded
Semantic ID	noether/combin/Tableau@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/category/test_category.py:15 · validation/unit/combin/test_acceptance_workload.py:30 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106

combin · Tableau¶

Worked example¶

combin.Tableau¶

combin.Tableau.__eq__¶

combin.Tableau.content¶

combin.Tableau.from_json¶

combin.Tableau.rows¶

combin.Tableau.rsk¶

combin.Tableau.semistandard¶

combin.Tableau.shape¶

combin.Tableau.to_json¶

`combin.Tableau`¶

`combin.Tableau.eq`¶

`combin.Tableau.content`¶

`combin.Tableau.from_json`¶

`combin.Tableau.rows`¶

`combin.Tableau.rsk`¶

`combin.Tableau.semistandard`¶

`combin.Tableau.shape`¶

`combin.Tableau.to_json`¶