Generalizing stack sorting and $c$-sorting for permutations, we define the permutree algorithm. Given two disjoint subsets $U$ $D$ of $\{2, \dots, n-1\}$, $(U,D)$-permutree tries to sort permutation $\pi \in \mathfrak{S}_n$ fails if only there are $1 \le i < j k n$ such that $\pi$ contains subword $jki$ $j U$ $kij$ D$. This algorithm is seen as a way explore an automaton which either rejects al...

How are proteins sorted to different destinations in eukaryotic cells? Until recently, it was generally thought that the constitutive flow of proteins to the cell surface occurs by default, and that proteins simply accumulate carbohydrate modifications as they pass sequentially through each compartment along the secretory pathway [1]. This hypothesis was supported by studies showing that inhibi...