Add full domain partition monoid method in semiex.gi,gd,tst

doc/semiex.xml

@@ -8,6 +8,25 @@
 #############################################################################
 ##
 
+<#GAPDoc Label="FullDomainPartitionMonoid">
+   <ManSection>
+    <Oper Name= "FullDomainPartitionMonoid" Arg = "n"/>
+    <Returns>A full domain partition monoid.</Returns>
+    <Description>
+      If <A>n</A> is a non-negative integer, then <C>FullDomainPartitionMonoid</C>
+      returns the full domain partition monoid of degree <A>n</A>. The <E>full domain partition monoid</E> is the subsemigroup of the partition monoid consisting of all bipartitions with their domain equal to <C>[1 .. n]</C> (the domain of a bipartition is defined in Chapter <Ref Chap="Bipartitions and blocks"/>, see <Ref Attr="DomainOfBipartition" />). As described in <Cite Key = "CarrollEastFresacher2026"/>
+
+    <Example><![CDATA[
+gap> S := FullDomainPartitionMonoid(5);
+<bipartition monoid of degree 5 with 4 generators>
+gap> Size(S);
+19921]]></Example>
+    </Description>
+  </ManSection>
+<#/GAPDoc>
+
+
+
 <#GAPDoc Label="EndomorphismsPartition">
    <ManSection>
     <Oper Name = "EndomorphismsPartition" Arg = "list"/>

doc/z-chap07.xml

@@ -68,6 +68,7 @@
     <#Include Label = "PlanarPartitionMonoid">
     <#Include Label = "ModularPartitionMonoid">
     <#Include Label = "ApsisMonoid">
+    <#Include Label = "FullDomainPartitionMonoid"/>
   </Section>
 
   <!--**********************************************************************-->

gap/semigroups/semiex.gd

@@ -74,6 +74,8 @@ DeclareOperation("SingularPlanarPartitionMonoid", [IsPosInt]);
 DeclareOperation("ModularPartitionMonoid", [IsPosInt, IsPosInt]);
 DeclareOperation("SingularModularPartitionMonoid", [IsPosInt, IsPosInt]);
 
+DeclareOperation("FullDomainPartitionMonoid", [IsInt]);
+
 # Matrix over finite field semigroups
 
 DeclareOperation("GeneralLinearMonoid", [IsPosInt, IsPosInt]);

gap/semigroups/semiex.gi

@@ -1353,6 +1353,28 @@ function(n)
   return Monoid(UnitriangularBooleanMatMonoid(n), gens);
 end);
 
+InstallMethod(FullDomainPartitionMonoid, "for an integer",
+[IsInt],
+function(n)
+  local gens;
+
+  if n < 0 then
+    ErrorNoReturn("the argument (an int) is not >= 0");
+  elif n = 0 then
+    return Monoid(Bipartition([]));
+  elif n = 1 then
+    return Monoid(Bipartition([[1], [-1]]));
+  fi;
+
+  gens := List(GeneratorsOfGroup(SymmetricGroup(n)), x -> AsBipartition(x, n));
+  Add(gens, Bipartition(Concatenation([[1, 2, -1, -2]],
+                                         List([3 .. n], x -> [x, -x]))));
+  Add(gens, Bipartition(Concatenation([[1, 2, -2], [-1]],
+                                         List([3 .. n], x -> [x, -x]))));
+
+  return Monoid(gens);
+end);
+
 #############################################################################
 ## 3. Standard examples - calculated generators
 #############################################################################

tst/standard/semigroups/semiex.tst

@@ -2008,6 +2008,23 @@ gap> S := TriangularBooleanMatMonoid(n);
 gap> Size(S);
 64
 
+#Test FullDomainPartitionMonoid
+gap> FullDomainPartitionMonoid(-1);
+Error, the argument (an int) is not >= 0
+gap> FullDomainPartitionMonoid(0);
+<trivial block bijection group of degree 0 with 1 generator>
+gap> FullDomainPartitionMonoid(1);
+<commutative bipartition monoid of degree 1 with 1 generator>
+gap> FullDomainPartitionMonoid(5);
+<bipartition monoid of degree 5 with 4 generators>
+gap> Size(FullDomainPartitionMonoid(5));
+19921
+gap> Size(FullDomainPartitionMonoid(4)) = Sum([1 .. 4], i -> 
+>                                              Sum([i .. 4], j -> Stirling2(4, i) *
+>                                                  Stirling2(4, j) * Factorial(j) /
+>                                                   Factorial(j - i)));
+true
+
 # Test ReflexiveBooleanMatMonoid
 gap> ReflexiveBooleanMatMonoid(1);
 <trivial group of 1x1 boolean matrices with 1 generator>