Knotted list structures

In (3) Perlis and Thornton describe a list structure language the central innovation of which is that the last word of each list specifies the location of the head of the list of which it is the terminal word. They call such list structures threaded ...

For any given k, the sequence of k-ary Catalan numbers, C"t","k=1kt+1(ktt), enumerates a number of combinatorial objects, including k-ary Dyck words of length n=kt and k-ary trees with t internal nodes. We show that these objects can be efficiently ...

Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible generalization of the Catalan numbers. We will present a new combinatorial object that is enumerated by the k-Catalan numbers, staircase tilings. We give a ...