15,313 reputation
23062
bio website nd.edu/~lnicolae
location University of Notre Dame
age 49
visits member for 2 years, 11 months
seen 19 mins ago
I do mostly geometry and topology, with an analytic bias. For the past few years Morse theory has popped up in my research, but not in a conventional way.

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comment A game of stones
I think that in your claim(s) you need to require that $q+1\geq 3$.
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comment A game of stones
@AaronMeyerowitz That is nice!
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comment A game of stones
@IanMorris I could not follow the Game of Thrones. After a season there were too many characters to process. However, I book titled A storm of surds sounds very intriguing.
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comment A game of stones
@Per Alexandersson I have added a remark to my original question shown that the nature of the jump $n\to n^2$ ought to play a role if the answer is positive.
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comment A game of stones
@Per your argument is an induction over the number $k$ of overcrowded nodes. What happens when there is exactly one overcrowded node, with lots of stones.
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comment A game of stones
@Andrew This is the key case. Maybe Per ought to add some details.
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comment A game of stones
Your argument seems to work with $n^2$ replaced by a function $f(n)>n+1$.
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comment A game of stones
@ Anthony Yes, you are right.
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comment A game of stones
Thanks Vidit. I will have a look at that post.
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comment A game of stones
@ Matthias $s$ and $N$ are independent, and $N$ is meant to be very large.
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