How to get k-combinations from array in aggregation

A colleague asked me if it's possible to generate all combinations of 2 items for a given array using aggregation pipeline expression.  In other words, something that gives this:

> db.combos.find()
{_id:1, a:[ 1,2,3]}
> db.combos.aggregate({$project:{_id:0, pairs: <generate-all-pairs>}})
{pairs: [  [1,2], [1,3], [2,3] ]}

I'm always game to challenge aggregation so here is what I came up with for the <generate> expression for k=2:

{$reduce:{
   input:{$range:[0,{$size:"$a"}]}, 
   initialValue:[], 
   in:{$concatArrays:[ 
      "$$value", 
      {$let:{
         vars:{i:"$$this"},
         in:{$map:{
            input:{$range:[{$add:[1,"$$i"]},{$size:"$a"}]},
            in:[ {$arrayElemAt:["$a","$$i"]}, {$arrayElemAt:["$a","$$this"]}] }}
      }}
   ]}
}}

This is the aggregation equivalent of looping over the array elements and for each one looping over the remaining array elements to create the pairs.  If array is `a` it's:

pairs = [];
for (i=0; i<a.length; i++) {
      for (j=a[i+1]; j<a.length; j++) {
            pairs.push([ [a[i], a[j] ]);
      }
}

Aggregation expressions are pretty powerful.  I gave a talk about the power of expressions over arrays at MongoDB World and local events in 2017/2018:  if you missed it watch it HERE.