AssociatedPartition in GAP4.10.1

[rtange]

Minor point:
AssociatedPartition([]); gives an error message, but it should just give [] (as in GAP3).
Please delete or close this issue if this has already been corrected in GAP4.10.2.

My GAP banner:
 ┌───────┐   GAP 4.10.1 of 23-Feb-2019
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: i686-pc-cygwin-default32-kv3
 Configuration:  gmp 6.1.2, readline
 Loading the library and packages ...

[wucas]

I can reproduce this with GAP 4.10.2:

 ┌───────┐   GAP 4.10.2 of 19-Jun-2019
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-apple-darwin18.6.0-default64-kv3
 Configuration:  gmp 6.1.2
 Loading the library and packages ...
 Packages:   AClib 1.3.1, Alnuth 3.1.1, AtlasRep 2.1.0, AutoDoc 2019.05.20, AutPGrp 1.10, Browse 1.8.8, Carat 2.2.3, CRISP 1.4.4, Cryst 4.1.19, CrystCat 1.1.9, CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, 
             Forms 1.2.5, GAPDoc 1.6.2, genss 1.6.5, IO 4.6.0, IRREDSOL 1.4, LAGUNA 3.9.3, orb 4.8.2, Polenta 1.3.8, Polycyclic 2.14, PrimGrp 3.3.2, RadiRoot 2.8, recog 1.3.2, ResClasses 4.7.2, 
             SmallGrp 1.3, Sophus 1.24, SpinSym 1.5.1, TomLib 1.2.8, TransGrp 2.0.4, utils 0.63
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> AssociatedPartition([]);
Error, List Element: <list>[1] must have an assigned value in
  for j in [ 1 .. lambda[1] ] do
    if j <= lambda[k] then
        res[j] := k;
    else
        k := k - 1;
        while j > lambda[k] do
            k := k - 1;
        od;
        res[j] := k;
    fi;
od; at /Users/lucas/Projects/gap-4.10.2/lib/combinat.gi:2478 called from 
<function "AssociatedPartition">( <arguments> )
 called from read-eval loop at *stdin*:1
you can 'return;' after assigning a value

and also in the current master branch:

 ┌───────┐   GAP 4.12dev-267-gb877da9 of today
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-apple-darwin19.2.0-default64-kv8
 Configuration:  gmp 6.1.2, GASMAN
 Loading the library and packages ...
#I  DeclareGlobalFunction: too many arguments in /Users/lucas/Projects/gap-dev/gap/pkg/crisp-1.4.4/lib/util.gd:16
Syntax warning: Unbound global variable in /Users/lucas/Projects/gap-dev/gap/pkg/atlasrep/gap/utils.gi:44
        pos:= POSITION_FIRST_COMPONENT_SORTED( WidthUnicodeTable, ints[j] );
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Packages:   AClib 1.3.1, Alnuth 3.1.0, AtlasRep 1.5.1, AutoDoc 2019.02.22, AutPGrp 1.10, Browse 1.8.8, Carat 2.2.3, CRISP 1.4.4, Cryst 4.1.18, CrystCat 1.1.8, CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, 
             GAPDoc 1.6.2, IO 4.5.4, IRREDSOL 1.4, LAGUNA 3.9.2, Polenta 1.3.8, Polycyclic 2.14, PrimGrp 3.3.2, RadiRoot 2.8, ResClasses 4.7.1, SmallGrp 1.3, Sophus 1.24, SpinSym 1.5, TomLib 1.2.7, 
             TransGrp 2.0.4, utils 0.61
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> AssociatedPartition([]);
Error, List Element: <list>[1] must have an assigned value in
  for j in [ 1 .. lambda[1] ] do
    if j <= lambda[k] then
        res[j] := k;
    else
        k := k - 1;
        while j > lambda[k] do
            k := k - 1;
        od;
        res[j] := k;
    fi;
od; at /Users/lucas/Projects/gap-dev/gap/lib/combinat.gi:2479 called from 
<function "AssociatedPartition">( <arguments> )
 called from read-eval loop at *stdin*:1
type 'quit;' to quit to outer loop

[fingolfin]

The code in AssociatedPartition clearly does not take the empty set into account. It shouldn't be hard to write a patch to fix this, plus a test case. I've labelled this issue as "good first issue" now, in case some volunteers want to help out with it.