Add preliminary support for TwistedBipartitions

.mailmap

@@ -9,6 +9,8 @@ Joseph Edwards <[email protected]> Joe Edwards <80713360+Joseph-Edwards@user
 Joseph Edwards <[email protected]> Joseph Edwards <[email protected]>
 Luke Elliott <[email protected]> le27 <[email protected]>
 Fernando Flores Brito <[email protected]> Fernando Flores Brito <[email protected]>
+Matthias Fresacher <[email protected]>
+Matthias Fresacher <[email protected]>
 Tillman Froehlich <[email protected]> <[email protected]>
 Nick Ham <[email protected]>
 Robert Hancock <[email protected]> Robert Hancock <[email protected]>

PackageInfo.g

@@ -156,6 +156,15 @@ Persons := [
     IsAuthor      := true,
     IsMaintainer  := false,
     Email         := "[email protected]"),
+
+  rec(
+    LastName      := "Fresacher",
+    FirstNames    := "Matthias",
+    IsAuthor      := true,
+    IsMaintainer  := false,
+    Email         := "[email protected]",
+    WWWHome       := "https://staff.cdms.westernsydney.edu.au/~mfresacher/",
+    Institution   := "Western Sydney University"),
 
   rec(
     LastName      := "Ham",

gap/elements/bipart.gd

@@ -72,6 +72,8 @@ DeclareProperty("IsPartialPermBipartition", IsBipartition);
 
 DeclareOperation("PermLeftQuoBipartition", [IsBipartition, IsBipartition]);
 
+DeclareOperation("NrFloatingBlocks", [IsBipartition, IsBipartition]);
+
 # Collections
 DeclareAttribute("DegreeOfBipartitionCollection", IsBipartitionCollection);
 DeclareOperation("OneMutable", [IsBipartitionCollection]);

gap/elements/bipart.gi

@@ -1111,3 +1111,64 @@ function(coll)
 
   return TensorBipartitions(coll);
 end);
+
+InstallMethod(NrFloatingBlocks, "for bipartition and bipartition",
+[IsBipartition, IsBipartition],
+function(a, b)
+  local n, anr, fuse, fuseit, ablocks, bblocks, x, y, made_it, tab, nr, i;
+
+  n := DegreeOfBipartition(a);
+  anr := NrBlocks(a);
+
+  fuse := [1 .. anr + NrBlocks(b)];
+
+  fuseit := function(i)
+      while fuse[i] < i do
+      i := fuse[i];
+      od;
+      return i;
+  end;
+
+  ablocks := IntRepOfBipartition(a);
+  bblocks := IntRepOfBipartition(b);
+
+  for i in [1 .. n] do
+      x := fuseit(ablocks[i + n]);
+      y := fuseit(bblocks[i] + anr);
+      if x <> y then
+      if x < y then
+          fuse[y] := x;
+      else
+          fuse[x] := y;
+      fi;
+      fi;
+  od;
+
+  made_it := BlistList(fuse, []);
+  for i in [1 .. n] do
+      made_it[fuseit(ablocks[i])] := true;
+  od;
+
+  for i in [n + 1 .. 2 * n] do
+      made_it[fuseit(bblocks[i] + anr)] := true;
+  od;
+  tab := 0 * fuse;
+  nr := 0;
+
+  for i in [n + 1 .. 2 * n] do
+      x := fuseit(ablocks[i]);
+      if not made_it[x] and tab[x] = 0 then
+      nr := nr + 1;
+      tab[x] := 1;
+      fi;
+  od;
+
+  for i in [1 .. n] do
+      x := fuseit(bblocks[i] + anr);
+      if not made_it[x] and tab[x] = 0 then
+      nr := nr + 1;
+      tab[x] := 1;
+      fi;
+  od;
+  return nr;
+end);

gap/elements/twisted-bipart.gd

@@ -0,0 +1,107 @@
+############################################################################
+##
+##  elements/twisted-bipart.gd
+##  Copyright (C) 2025                                   James D. Mitchell
+##
+##  Licensing information can be found in the README file of this package.
+##
+#############################################################################
+##
+## In collaboration with
+##
+##############################################
+##                                          ##
+##               Code created               ##
+##                    by                    ##
+##          *--------------------*          ##
+##          | Matthias Fresacher |          ##
+##          *--------------------*          ##
+##                                          ##
+##############################################
+
+#    *------------------------------*
+#    |``````````````````````````````|
+#    |`````____````____`````````````|
+#    |````|MFMF\  /MFMF|````````````|
+#    |````|MF|MF\/MF|MF|````````````|
+#    |````|MF|\MFMF/|MF|_______`````|
+#    |````|MF|``````|MFMFMFMFMF|````|
+#    |````|MF|``````|MF|````````````|
+#    |````|MF|``````|MF|___`````````|
+#    |``````````````|MFMFMF|````````|
+#    |``````````````|MF|````````````|
+#    |``````````````|MF|````````````|
+#    |``````````````|MF|````````````|
+#    |``````````````````````````````|
+#    *------------------------------*
+
+DeclareCategory("IsTwistedBipartition", IsMultiplicativeElementWithOne
+and IsMultiplicativeElementWithZero and
+IsAssociativeElement);
+DeclareCategoryCollections("IsTwistedBipartition");
+DeclareCategoryCollections("IsTwistedBipartitionCollection");
+
+DeclareOperation("TwistedBipartition", [IsInt, IsBipartition, IsInt]);
+DeclareOperation("ZeroTwistedBipartition", [IsInt, IsInt]);
+DeclareAttribute("DegreeOfTwistedBipartition",
+IsTwistedBipartition);
+DeclareAttribute("DegreeOfTwistedBipartitionCollection",
+IsTwistedBipartitionCollection);
+DeclareAttribute("MaxFloatingBlocks",
+IsTwistedBipartition);
+DeclareAttribute("NrFloatingBlocks",
+IsTwistedBipartition);
+DeclareAttribute("UnderlyingBipartition",
+IsTwistedBipartition);
+DeclareAttribute("UnderlyingBipartitionCollection",
+IsTwistedBipartitionCollection);
+
+DeclareOperation("RandomNonZeroTwistedBipartition", [IsInt, IsInt]);
+DeclareOperation("RandomNonZeroTwistedBipartition", [IsRandomSource, IsInt, IsInt]);
+DeclareOperation("RandomTwistedBipartition", [IsInt, IsInt]);
+DeclareOperation("RandomTwistedBipartition", [IsRandomSource, IsInt, IsInt]);
+DeclareProperty("IsZero", IsTwistedBipartition);
+DeclareProperty("IsOne", IsTwistedBipartition);
+DeclareOperation("IdentityTwistedBipartition", [IsPosInt, IsInt]);
+DeclareAttribute("ZeroImmutable", IsTwistedBipartition);
+
+DeclareAttribute("DegreeOfBipartition", IsTwistedBipartition);
+DeclareAttribute("NrBlocks", IsTwistedBipartition);
+DeclareAttribute("NrLeftBlocks", IsTwistedBipartition);
+DeclareAttribute("NrRightBlocks", IsTwistedBipartition);
+DeclareAttribute("RankOfBipartition", IsTwistedBipartition);
+
+DeclareAttribute("DomainOfBipartition", IsTwistedBipartition);
+DeclareAttribute("CodomainOfBipartition", IsTwistedBipartition);
+
+DeclareAttribute("NrTransverseBlocks", IsTwistedBipartition);
+DeclareOperation("OneMutable", [IsTwistedBipartition, IsInt]);
+DeclareOperation("OneMutable", [IsTwistedBipartitionCollection, IsInt]);
+
+DeclareProperty("IsBlockBijection", IsTwistedBipartition);
+DeclareProperty("IsUniformBlockBijection", IsTwistedBipartition);
+DeclareProperty("IsPartialPermBipartition", IsTwistedBipartition);
+DeclareProperty("IsTransBipartition", IsTwistedBipartition);
+DeclareProperty("IsDualTransBipartition", IsTwistedBipartition);
+DeclareProperty("IsPermBipartition", IsTwistedBipartition);
+
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPerm, IsZeroCyc, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPerm, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPerm, IsPosInt, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPartialPerm, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPartialPerm, IsZeroCyc, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsPartialPerm, IsPosInt, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsTransformation, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsTransformation, IsPosInt, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsTransformation, IsZeroCyc, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsBipartition, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsBipartition, IsPosInt, IsInt]);
+DeclareOperation("AsTwistedBipartition", [IsTwistedBipartition]);
+DeclareOperation("AsTwistedBipartition", [IsTwistedBipartition, IsPosInt]);
+DeclareOperation("AsTwistedBipartition", [IsInt, IsBipartition, IsZeroCyc, IsInt]);
+# DeclareOperation("AsTwistedBipartition", [IsInt, IsPBR, IsZeroCyc, IsInt]);
+# DeclareOperation("AsTwistedBipartition", [IsInt, IsPBR, IsPosInt, IsInt]);
+# DeclareOperation("AsTwistedBipartition", [IsInt, IsPBR, IsInt]);
+
+DeclareOperation("AsBlockBijection", [IsTwistedBipartition, IsPosInt]);
+DeclareOperation("AsBlockBijection", [IsTwistedBipartition]);