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  • 1
    Electronic Resource
    Electronic Resource
    Some Problems and Results on Combinatorial Number Theory (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 576 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb16392.x
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  • 2
    Electronic Resource
    Electronic Resource
    Multipartite Graph-Tree Ramsey Numbers (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 576 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb16393.x
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  • 3
    Electronic Resource
    Electronic Resource
    An Extremal Result for Paths (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 576 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb16394.x
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  • 4
    Electronic Resource
    Electronic Resource
    Density functions for prime and relatively prime numbers (1977)
    Springer
    Monatshefte für Mathematik 83 (1977), S. 99-112 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Letr *(x) denote the maximum number of pairwiserelatively prime integers which can exist in an interval (y,y+x] of lengthx, and let ϱ*(x) denote the maximum number ofprime integers in any interval (y,y+x] wherey≥x. Throughout this paper we assume the “primek-tuples hypothesis.” (This hypothesis could be avoided by using an alternative sievetheoretic definition of ϱ*(x); cf. the beginning of Section 1.) We investigate the differencer *(x)—ϱ*(x): that is we ask how many more relatively prime integers can exist on an interval of lengthx than the maximum possible number of prime integers. As a lower bound we obtainr *(x)—ϱ*(x)〈x c for somec〉0 (whenx→∞). This improves the previous lower bound of logx. As an upper bound we getr *(x)—ϱ*(x)=o[x/(logx)2]. It is known that ϱ*(x)—π(x)〉const.[x/(logx)2];.; thus the difference betweenr *(x) and ϱ*(x) is negligible compared to ϱ*(x)—π(x). The results mentioned so far involve the “upper bound” or “maximizing” sieve. In Section 2, similar comparisons are made between two types of “minimum” sieves. One of these is the “erasing” sieve, which completely eliminates an interval of lengthx; and the other, introduced by Erdös and Selfridge [1], involves a kind of “minimax” for sets of pairwise relatively prime numbers. Again these two sieving methods produce functions which are found to be closely related.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01534631
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  • 5
    Electronic Resource
    Electronic Resource
    Repeated distances in space (1988)
    Springer
    Graphs and combinatorics 4 (1988), S. 207-217 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Fori = 1,...,n letC(xi, ri) be a circle in the plane with centrex i and radiusr i. A repeated distance graph is a directed graph whose vertices are the centres and where (x i, xj) is a directed edge wheneverx j lies on the circle with centrex i. Special cases are the nearest neighbour graph, whenr i is the minimum distance betweenx i and any other centre, and the furthest neighbour graph which is similar except that maximum replaces minimum. Repeated distance graphs generalize to any dimension with spheres or hyperspheres replacing circles. Bounds are given on the number of edges in repeated distance graphs ind dimensions, with particularly tight bounds for the furthest neighbour graph in three dimensions. The proofs use extremal graph theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01864161
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  • 6
    Electronic Resource
    Electronic Resource
    On Locally Repeated Values of Certain Arithmetic Functions, IV (1997)
    Springer
    The Ramanujan journal 1 (1997), S. 227-241 
    Details
    ISSN: 1572-9303
    Keywords: Turán-Kubilius inequality ; additive functions ; prime divisors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let ω(n) denote the number of prime divisors of n and let Ω(n) denote the number of prime power divisors of n. We obtain upper bounds for the lengths of the longest intervals below x where ω(n), respectively Ω(n), remains constant. Similarly we consider the corresponding problems where the numbers ω(n), respectively Ω(n), are required to be all different on an interval. We show that the number of solutions g(n) to the equation m+ω(m)=n is an unbounded function of n, thus answering a question posed in an earlier paper in this series. A principal tool is a Turán-Kubilius type inequality for additive functions on arithmetic progressions with a large modulus.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009723712317
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  • 7
    Electronic Resource
    Electronic Resource
    On admissible constellations of consecutive primes (1988)
    Springer
    BIT 28 (1988), S. 391-396 
    Details
    ISSN: 1572-9125
    Keywords: Primary 11A41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Admissible constellations of primes are patterns which, like the twin primes, no simple divisibility relation would prevent from being repeated indefinitely in the series of primes. All admissible constellations, formed ofconsecutive primes, beginning with a prime 〈1000, are established, and some properties of such constellations in general are conjectured.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01941122
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  • 8
    Electronic Resource
    Electronic Resource
    Convex nonagons with five intervertex distances (1996)
    Springer
    Geometriae dedicata 60 (1996), S. 317-332 
    Details
    ISSN: 1572-9168
    Keywords: 52C05 ; 52C10 ; 52B05 ; convex nonagons ; intervertex distances ; lattice theory ; Erdös conjecture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n≥7, the samllest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00147368
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  • 9
    Electronic Resource
    Electronic Resource
    OnTaylor series of functions regular inGaier regions (1954)
    Springer
    Archiv der Mathematik 5 (1954), S. 39-52 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01899316
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  • 10
    Electronic Resource
    Electronic Resource
    On the largest prime factors ofn andn + 1 (1978)
    Springer
    Aequationes mathematicae 17 (1978), S. 115-115 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01818551
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