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</script>A fork stack is a generalised stack which allows pushes and pops of several items at a time. We consider the problem of determining which input streams can be sorted using a single forkstack, or dually, which permutations of a fixed input stream can be produced using a single forkstack. An algorithm is given to solve the sorting problem and the minimal unsortable sequences are found. The results are extended to fork stacks where there are bounds on how many items can be pushed and popped at one time. In this context we also establish how to enumerate the collection of sortable sequences.
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), sortable sequences, Exact enumeration problems, generating functions, Combinatorics in computer science, G.2.1, permutation, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), sortable sequences, Exact enumeration problems, generating functions, Combinatorics in computer science, G.2.1, permutation, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), Computer Science - Discrete Mathematics
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