I think I heard the “become grand meta-theorem” phrasing originally from Alon & Spencer. I actually bought the Flajolet and Sedgewick book a couple months ago (only got through the first chapter), but it was mind-boggling that something like this could be done for combinatorics.
Of course reality is self-similar, so it’s not surprising that there’s currently a big divide in combinatorics between what I would call the “algebraic/enumerative” style of Richard Stanley containing the Flajolet and Sedgewick stuff, characterized by fancy algebra/explicit formulae/crystalline structures and the “analytic/extremal” style of Erdos, characterized by asymptotic formulae and less legibility. It’s surprisingly rare to see a combinatorialist bridge this gap.
I went through most of the first half of Flajolet and Sedgewick when I was 18 or so and was blown away, then recently went through the second half and was blown away in a completely different way. It’s really wild. Take a look. It’s where I learned the argument in this blog post about the asymptotics of the partition function.
I think I heard the “become grand meta-theorem” phrasing originally from Alon & Spencer. I actually bought the Flajolet and Sedgewick book a couple months ago (only got through the first chapter), but it was mind-boggling that something like this could be done for combinatorics.
Of course reality is self-similar, so it’s not surprising that there’s currently a big divide in combinatorics between what I would call the “algebraic/enumerative” style of Richard Stanley containing the Flajolet and Sedgewick stuff, characterized by fancy algebra/explicit formulae/crystalline structures and the “analytic/extremal” style of Erdos, characterized by asymptotic formulae and less legibility. It’s surprisingly rare to see a combinatorialist bridge this gap.
I went through most of the first half of Flajolet and Sedgewick when I was 18 or so and was blown away, then recently went through the second half and was blown away in a completely different way. It’s really wild. Take a look. It’s where I learned the argument in this blog post about the asymptotics of the partition function.