MathOverflow

Given $n$ nodes uniformly distributed in $[0,1]^2$, consider the nearest neighbor algorithm to solve traveling salesman problem, i.e., each time I select the nearest neighbor not visited so far as the next node to visit, my question is: what is the expected...

I remember a friend in graduate school throwing an early edition of Jurgen Neukirch's Algebraic Number Theory book against a wall (so hard that it split the binding) after he had worked for a number of days to reconcile something he realized was an error...

This is a follow up on question Is Z + Functionality interpretable by ZFC?
The idea here is to produce a violation of the answer given there by trying to force indefinable functions. So, I'll proceed in the same style:
Starting with $\sf Z$ minus Separation, add to its language a primitive constant $0$ standing for the empty set, and primitive total $(n+1)$-ary functions $f^n_i$ where $i$ is a natural, now let $\varphi_0, \varphi_1, \cdots$ be an enumeration on formulas...

With the luck of intuition, I conjecture that $$ {n+m+1 \brack m+1} = (-1)^n \sum\limits_{k=0}^{n} \left[ \left[ \sum\limits_{i=0}^{k} (-1)^{k+i} 2^{k-i} \binom{n+k}{k-i} {n+i \brace i} \right] \cdot \left[ \sum\limits_{j=k}^{n} (-1)^j \binom{n+j}{n...