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Convergence to the Poisson distribution, for the number of occurrences of dependent events, can often be established by computing only first and second moments, but not higher ones. This remarkableâ€¦ (More)

- Richard Arratia
- Electr. J. Comb.
- 1999

Consider, for a permutation Ïƒ âˆˆ Sk, the number F (n, Ïƒ) of permutations in Sn which avoid Ïƒ as a subpattern. The conjecture of Stanley and Wilf is that for every Ïƒ there is a constant c(Ïƒ) < âˆž suchâ€¦ (More)

- Richard Arratia, BÃ©la BollobÃ¡s, Gregory B. Sorkin
- J. Comb. Theory, Ser. B
- 2004

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable " interlace polynomial " for any graph. The polynomial satisfies a beautiful and unexpected reductionâ€¦ (More)

- Richard Arratia, BÃ©la BollobÃ¡s, Gregory B. Sorkin
- SODA
- 2000

We define a new graph polynomial, the interlace polynomial, for any undirected graph. Also, we show how to count Euler circuits and circuit decompositions for any directed or undirected Eulerianâ€¦ (More)

The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be givenâ€¦ (More)

- Michael S. Waterman, Richard Arratia, David J. Galas
- Bulletin of mathematical biology
- 1984

The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themesâ€¦ (More)

- Richard Arratia, BÃ©la BollobÃ¡s, Gregory B. Sorkin
- Combinatorica
- 2004

Generalizing a previous one-variable " interlace polynomial " , we consider a new interlace polynomial in two variables. The polynomial can be computed in two very different ways. The first is anâ€¦ (More)

- Richard Arratia, Daniel Martin, Gesine Reinert, Michael S. Waterman
- Journal of Computational Biology
- 1996

Sequencing by hybridization is a tool to determine a DNA sequence from the unordered list of all l-tuples contained in this sequence; typical numbers for l are l = 8, 10, 12. For theoretical purposesâ€¦ (More)

- Richard Arratia, Louis I. Gordon
- Bulletin of mathematical biology
- 1989

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability of k or more successes in n independent trials, each with successâ€¦ (More)

- Richard Arratia, Eric S. Lander, Simon TavarÃ©, Michael S. Waterman
- Genomics
- 1991

A complete physical map of the DNA of an organism, consisting of overlapping clones spanning the genome, is an extremely useful tool for genomic analysis. Various methods for the construction of suchâ€¦ (More)