Quoting Gian-Carlo Rota (from the Foreword to Richard Stanley's Enumerative Combinatorics Volume I), "In mathematics, however, the burden of choice faced by the writer is so heavy as to turn off all but the most courageous. And of all mathematics, combinatorics is nowadays perhaps the hardest to write on, despite an eager audience... Shall the author yield to one of the contrary temptations of recreational math at one end, and categorical rigor at the other? or to the highly rewarding lure of the algorithm?"
Does anyone understand this last statement? What is the lure of the algorithm? Is it a reference to something particular?
I am sometimes quite happy to attain an elegant algorithm, but when it comes to writing I tend to leave the details of hard-to-formalize algorithms to the reader (e.g. "We omit the proof that this establishes the desired bijection."). And if there is a "lure", I cannot think of any example to substantiate Rota's slightly derisive tone. I admire authors who contribute algorithmic intuition to the literature. In Stanley's own book (Volume II) is an impeccable discussion of algorithms concerning the enumeration of rooted trees.