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  • 1
    Digitale Medien
    Digitale Medien
    How likely is Polya's drunkard to stay in x⩾ y⩾z? (1989)
    Springer
    Journal of statistical physics 57 (1989), S. 1129-1135 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Restricted random walk ; method of images ; return probability ; linear partial recurrence equations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inx⩾y⩾z. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01020052
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  • 2
    Digitale Medien
    Digitale Medien
    Enumeration Schemes and, more importantly, their automatic generation (1998)
    Springer
    Annals of combinatorics 2 (1998), S. 185-195 
    Details
    ISSN: 0219-3094
    Schlagwort(e): 05A15 ; Permutation with restricted positions ; Automated proofs in combinatorics ; Wilf classes
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The notion of Enumeration Scheme is introduced and applied to the problem of counting permutations with forbidden patterns. Most importantly, the process is completely automated in a software package, WILF, accompanying this article.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01608488
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  • 3
    Digitale Medien
    Digitale Medien
    An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities (1992)
    Springer
    Inventiones mathematicae 108 (1992), S. 575-633 
    Details
    ISSN: 1432-1297
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary It is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here. We give many examples of the method, including computer-generated proofs of identities of Mehta-Dyson, Selberg, Hille-Hardy,q-Saalschütz, and others. The prospect of using the method for proving multivariate identities that involve an arbitrary number of summations/integrations is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02100618
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  • 4
    Digitale Medien
    Digitale Medien
    A Markov chain occurring in enzyme kinetics (1982)
    Springer
    Journal of mathematical biology 15 (1982), S. 351-357 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Markov chain ; Steady state probabilities ; Catalan numbers ; Sequence enumeration ; Enzyme kinetics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275693
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  • 5
    Buch
    Buch
    ¬A¬ equals B ; ¬A¬ = B (1996)
    Wellesley, MA :A. K. Peters,
    Details
    Titel: ¬A¬ equals B ; ¬A¬ = B
    Autor: Petkovsek, Marko
    Beteiligte Person(en): Wilf, Herbert S. , Zeilberger, Doron
    Verlag: Wellesley, MA :A. K. Peters,
    Erscheinungsjahr: 1996
    Seiten: 212 S.
    Materialart: Buch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    Zuse-Institut Berlin get availability status
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