This is a result of Singmaster (American Math Monthly, 1971).
Here is his proof ($N(a)$ is the number of times $a$ appears.) This result has since been much improved, see the wikipedia article on Singmaster's conjecture.
To elaborate somewhat, Abbott-Erdos-Hanson show:
and use this to show the better asymptotic bound. It is not quite clear how to use this to get better bounds for all $t.$
This is a result of Singmaster (American Math Monthly, 1971).
Here is his proof ($N(a)$ is the number of times $a$ appears.) This result has since been much improved, see the wikipedia article on Singmaster's conjecture.
This is a result of Singmaster (American Math Monthly, 1971).
Here is his proof ($N(a)$ is the number of times $a$ appears.) This result has since been much improved, see the wikipedia article on Singmaster's conjecture.
To elaborate somewhat, Abbott-Erdos-Hanson show:
and use this to show the better asymptotic bound. It is not quite clear how to use this to get better bounds for all $t.$
This is a result of Singmaster (American Math Monthly, 1971).
Here is his proof ($N(a)$ is the number of times $a$ appears.) This result has since been much improved, see the wikipedia article on Singmaster's conjecture.
