5 problems

Quadrangulation conjecture. There is an explicit bijection preserving genus and number of edges between rooted quadrangulations and rooted maps with certain decorations that proves…

An alternating sign matrix (ASM) is an $n\times n$ matrix with entries in $\{0,1,-1\}$ such that, in each row and each column, the nonzero entries alternate and sum to $1$. Robbins…

Babson–Steingrímsson's conjecture. The distribution of the bistatistic $(des,stat)$ is equal to that of $(des,maj)$.

Oscillating-tableau conjecture. Oscillating tableaux of height bounded by $k$ ending in a row are in bijection with Young tableaux of bounded height $2k$.

The missing lemma. Condition (i) of Theorem holds for these parameters.