8,008 research outputs found
Wolstenholme and Morley, Primes and Pseudoprimes
In this note, we prove is a Morley pseudoprime (of order 2) iff
is a Wolstenholme pseudoprime (of order 2) iff is a Wolstenholme prime iff
is a Morley prime. Concerning pseudoprimes of order 1 that are not powers
of primes, only 3 are known of Wolstenholme's type and absolutely none have yet
been identified of Morley's type
Simple closed form Hankel transforms based on the central coefficients of certain Pascal-like triangles
We study the Hankel transforms of sequences related to the central
coefficients of a family of Pascal-like triangles. The mechanism of Riordan
arrays is used to elucidate the structure of these transforms
Why Delannoy numbers?
This article is not a research paper, but a little note on the history of
combinatorics: We present here a tentative short biography of Henri Delannoy,
and a survey of his most notable works. This answers to the question raised in
the title, as these works are related to lattice paths enumeration, to the
so-called Delannoy numbers, and were the first general way to solve Ballot-like
problems. These numbers appear in probabilistic game theory, alignments of DNA
sequences, tiling problems, temporal representation models, analysis of
algorithms and combinatorial structures.Comment: Presented to the conference "Lattice Paths Combinatorics and Discrete
Distributions" (Athens, June 5-7, 2002) and to appear in the Journal of
Statistical Planning and Inference
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