Converts an alternating sign matrix (ASM) to a monotone triangle according to the bijection described in [HR]. More precisely, suppose $A$ is an ASM. The unique monotone triangle $T=(T_0,\ldots,T_n)$ corresponding to $A$ has the property that $T_m$ is the (ordered) set of column indices in which $\sum_{i=1}^m A_m $ has an entry of $1$, where $A_m$ denotes the $m$th row of $A$. See [HR] for more details.
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The object ASMToMonotoneTriangle is a method function.