On Alternating Multiple Sums (Malte Henkel and R. A. Weston)
نویسندگان
چکیده
منابع مشابه
A note on alternating sums
We present some results on a certain type of alternating sums which frequently arise in connection with the average-case analysis of algorithms and data structures. Whereas the so-called Rice's method for treating such sums uses complex contour integration we perform manipulations of generating functions in order to get explicit results from which asymptotic estimates follow immediately.
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By convention we set H(s;n) = 0 any n < d. We call l(s) := d and |s| := ∑d i=1 |si| its depth and weight, respectively. We point out that l(s) is sometimes called length in the literature. When every si is positive we recover the multiple harmonic sums (MHS for short) whose congruence properties are studied in [9, 10, 17, 18]. There is another “non-strict” version of the AMHS defined as follows...
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We show that for any prime prime p = 2, p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the left-hand side as a combination of alternating multiple harmonic sums.
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The well-known Wolstenholme’s Theorem says that for every prime p > 3 the (p−1)-st partial sum of the harmonic series is congruent to 0 modulo p2. If one replaces the harmonic series by ∑ k≥1 1/n for k even, then the modulus has to be changed from p2 to just p. One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partia...
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Abstract We discuss several well known results about Schur functions that can be proved using cancellations in alternating summations; notably we shall discuss the Pieri and Murnaghan-Nakayama rules, the JacobiTrudi identity and its dual (Von Nägelsbach-Kostka) identity, their proofs using the correspondence with lattice paths of Gessel and Viennot, and finally the Littlewood-Richardson rule. O...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 1993
ISSN: 0036-1445,1095-7200
DOI: 10.1137/1035101