4 problems

Conjecture. There exist an absolute constant $c\ge 1$ and an online algorithm such that, for every finite matroid $M$ and every choice of nonnegative weights, the algorithm selects…

In the two-sided secretary game, suppose there are $U$ men and $U$ women, each player meets $N$ partners over $N$ rounds, and preferences satisfy universal rank symmetry: if a man…

In the cooperative two-sided secretary game, let $N$ be the number of rounds and let $R_N(1)$ denote the expected $N$-rank of a player entering the game, under an optimal common st…

Secretary problem conjecture. There is an algorithm for the secretary problem on $(P,\prec)$ that is successful with probability at least $p_k$.