examples: add catalan_monoid

Author: codex

docs/source/data-structures/presentations/examples.rst

@@ -30,6 +30,7 @@ semigroup or monoid they define.
     alternating_group
     braid_group
     brauer_monoid
+    catalan_monoid
     chinese_monoid
     cyclic_inverse_monoid
     dual_symmetric_inverse_monoid

src/libsemigroups_pybind11/presentation/examples.py

@@ -19,6 +19,7 @@
     presentation_examples_braid_group as _braid_group,
     presentation_examples_brauer_monoid as _brauer_monoid,
     presentation_examples_brauer_monoid_KM07 as _brauer_monoid_KM07,
+    presentation_examples_catalan_monoid as _catalan_monoid,
     presentation_examples_chinese_monoid as _chinese_monoid,
     presentation_examples_chinese_monoid_CEKNH01 as _chinese_monoid_CEKNH01,
     presentation_examples_cyclic_inverse_monoid as _cyclic_inverse_monoid,
@@ -105,6 +106,7 @@
 brauer_monoid = _wrap_cxx_free_fn(_brauer_monoid)
 braid_group = _wrap_cxx_free_fn(_braid_group)
 brauer_monoid_KM07 = _wrap_cxx_free_fn(_brauer_monoid_KM07)
+catalan_monoid = _wrap_cxx_free_fn(_catalan_monoid)
 chinese_monoid = _wrap_cxx_free_fn(_chinese_monoid)
 chinese_monoid_CEKNH01 = _wrap_cxx_free_fn(_chinese_monoid_CEKNH01)
 cyclic_inverse_monoid = _wrap_cxx_free_fn(_cyclic_inverse_monoid)

src/presentation-examples.cpp

@@ -1888,6 +1888,26 @@ defines a monoid of size :math:`C_n d^n` where :math:`C_n` is the
 :raises LibsemigroupsError:  if ``n < 3`` or if ``d == 0``.
 
 .. seealso::  :any:`abacus_jones_monoid_AJP25`.
+)pbdoc");
+
+    m.def("presentation_examples_catalan_monoid",
+          &examples::catalan_monoid,
+          py::arg("n"),
+          R"pbdoc(
+:sig=(n: int) -> Presentation:
+A presentation for the Catalan monoid.
+
+This function returns a monoid presentation defining the Catalan monoid of
+degree *n*, using the standard generators :math:`e_1, \ldots, e_{n - 1}` and
+their standard defining relations.
+
+:param n: the degree.
+:type n: int
+
+:returns: The specified presentation.
+:rtype: Presentation
+
+:raises LibsemigroupsError:  if ``n < 1``.
 )pbdoc");
 
     m.def("presentation_examples_abacus_jones_monoid_AJP25",

tests/test_presentation_examples.py

@@ -8,7 +8,7 @@
 
 # pylint: disable=missing-function-docstring, invalid-name
 
-from math import factorial
+from math import comb, factorial
 
 import pytest
 
@@ -67,6 +67,7 @@ def test_monoid_status():
 
     assert examples.alternating_group_Moo97(5).contains_empty_word()
     assert examples.brauer_monoid_KM07(5).contains_empty_word()
+    assert examples.catalan_monoid(5).contains_empty_word()
     assert examples.chinese_monoid_CEKNH01(5).contains_empty_word()
     assert examples.cyclic_inverse_monoid_Fer22_a(5).contains_empty_word()
     assert examples.cyclic_inverse_monoid_Fer22_b(5).contains_empty_word()
@@ -163,6 +164,19 @@ def test_full_transformation_monoid():
     check_full_transformation_monoid([2], examples.full_transformation_monoid)
 
 
+def test_catalan_monoid():
+    ReportGuard(False)
+    with pytest.raises(LibsemigroupsError):
+        examples.catalan_monoid(0)
+
+    n = 5
+    p = examples.catalan_monoid(n)
+    p.throw_if_bad_alphabet_or_rules()
+
+    tc = ToddCoxeter(congruence_kind.twosided, p)
+    assert tc.number_of_classes() == comb(2 * n, n) // (n + 1)
+
+
 def test_partial_transformation_monoid_Shu60():
     ReportGuard(False)
     with pytest.raises(LibsemigroupsError):