Titlebook: Number Theory and Discrete Mathematics; A. K. Agarwal,Bruce C. Berndt,Michel Waldschmidt Conference proceedings 2002 Springer Basel AG 200

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A Note on Cordial Labelings of Multiple Shells,(.). 0 and . (.) . respectively. Let .. (0), .. (1) be similarly defined. A graph is said to be . if there exists a vertex labeling . such that.and..In this paper, we show that every multiple shell.is cordial for all positive integers.

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978-3-0348-9481-4Springer Basel AG 2002

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Number Theory and Discrete Mathematics978-3-0348-8223-1Series ISSN 2297-0215 Series E-ISSN 2297-024X

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Multiple Polylogarithms: An Introduction,s the classical polylogarithm Li.(.). These multiple polylogarithms can be defined also in terms of iterated Chen integrals and satisfy . Multiple polylogarithms in several variables are defined for .. ≥ 1 and |..| < 1(1 ≤ . ≤. by., and they satisfy not only shuffle relations, but also . When one sp

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A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which Contain a Fixedith side lengths 2. +.,2. + ., .,. a, 2n + ., . contains the (horizontal) rhombus with coordinates (2n + x, 2n + y) is equal to .,where ..(n) . rational function in n. Several specific instances of this “1/3-phenomenon” are made explicit.

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,Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Pao establish a connection between three particular cases of these restricted Frobenius partition functions and Burge’s restricted partition pairs (.). This connection and Burge’s Theorem 1 give us three new analytic identities. A comparison of these analytic identities with three known identities fro

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Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs,. This is due to several reasons, two most important of which are the structural symmetry and the difficulty in constructions of these designs (compared to other classes of designs). The initial part of this exposition will concentrate on new results on symmetric designs. Quasi-symmetric designs are

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