Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
4 problems
How large must arithmetic circuits and formulas computing the n × n permanent be? New lower bounds include an arithmetic-formula bound of order n^4/log n, far beyond the quadratic barrier that stood for decades.
Can an S-decoding polynomial modulo a suitable product of k primes attain the lower-bound minimum of k + 1 nonzero coefficients? A construction matches the bound for special products of k primes, yielding exponentially fewer-server PIR.
What is the maximum size of a binary code of given minimum distance? The linear-programming bounds of McEliece, Rodemich, Rumsey and Welch (1977) resisted improvement for half a century. The new upper bounds are exponentially stronger at…
New upper and lower bounds on the approximation ratio achievable for Multiway Cut via large mixtures of new and old rounding schemes for the CKR relaxation, advancing the ratio ladder that has run since Călinescu-Karloff-Rabani (1998).