Fad over fatality? The hazards of amber teething necklaces

Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)

Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algoŽ . rit...

Efficient Indexing of Necklaces and Irreducible Polynomials over Finite Fields

We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1, . . . , |S|} and the set S of all irreducible, monic, univariate polynomials of degree n over a finite field Fq. This has applications in pseudorandomness, an...

Teething revisited.

Teething as a disease entity has been diminished from its 19th century status as the major cause of infant mortality to its modest position today as a "waste basket" diagnosis. If past proves to be prologue, it will diminish further as more credible causes for undifferentiated fevers and other complaints are found. The 21st century may find teething consigned to the shelf along with miasma, hum...

Late Teething in India

cut their teeth at a later age than that given in books. Out of 100 infants of varying ages, from 8 months to 2 years, 30, nearly one-third, had cut no teeth ; and out of 14 infants, S months' old, more than half, 8, had not commenced teething ; out of 27 infants one year old, 7 had not cut any tooth, 7 had cut 4, 6 had cut 6 teeth, and only one had 9. Though the statistics speak comparatively ...

Teething: facts and fiction.