Simple higher-order partial function that takes advantage of sparse arrays to make parameters skippable.

partial.js

function partial(fn, fixedArgs) {
  return function() {
    var args = fixedArgs.slice(), skipped = 0;
    for (var i = 0, n = arguments.length; i < n; i++) {
      while (i + skipped in args) { skipped++; }
      args[i + skipped] = arguments[i];
    }
    return fn.apply(this, args);
  };
}

usage.js

function f(a, b, c, d, e, f) { return [a, b, c, d, e, f] };

var fʹ = partial(f, [, 2, , 4, , 6]);
fʹ(1, 3, 5); // [1, 2, 3, 4, 5, 6]

var fʺ = partial(f, [1, 2, , , 5]);
fʺ(3, 4, 6); // [1, 2, 3, 4, 5, 6]