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We give efficient algorithms for ranking Lyndon words of length $n$ over an alphabet of size $\sigma$. The rank of a Lyndon word is its position in the sequence of lexicographically ordered Lyndon words of the same length. The outputs are integers of ...

This paper introduces the concept of necklace binomial coefficients motivated by the enumeration of a special type of sequences. Several properties of these coefficients are described, including a connection between their roots and an elliptic curve. ...

A de Bruijn sequence is a circular binary string of length 2ⁿ that contains each binary string of length n exactly once as a substring. A maximum-density de Bruijn sequence is a circular binary string of length n (n 0)+(n 1)+(n 2)+...+(n m) that ...

A k-ary necklace is an equivalence class of k-ary strings under rotation. A necklace of fixed density is a necklace where the number of zeros is fixed. We present a fast, simple, recursive algorithm for generating (i.e., listing) fixed-density k-ary ...

The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code ...

One of the first theorems on permutation routing, proved by V.E. Benes (1965), shows that give a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, ...

A Spanning Balancedn-tree (SBnT) in a Boolean n-cube is a spanning tree in which the root has fanout n, and all the subtrees of the root have $O({{2^n } / n})$ nodes. The number of tree edges in each dimension of the n-cube is of order $O({{2^n } / n})$...

It is often desirable in modern signal processing applications to perform two-dimensional or three-dimensional Fourier transforms. Until the advent of VLSI it was not possible to think about one chip implementation of such processes. In this paper ...