منابع مشابه
Reflections on Symmetric Polynomials and Arithmetic Functions
Abstract. In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and power sum symmetric polynomials. We investigate properties of these families and focus on constructing their rational roots under a product induce...
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Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the inverse of LOG. In particular, LOG takes a convolution product of generalized Fibonacci polynomials to a sum of generalized Lucas polynomials and EXP takes the sum to the convolution product. We use this structure to ...
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We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive to the combinatorics of partitions of the integers. The representing elements are recursive sequences of Schur polynomials evaluated at subrings of the comp...
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Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, if p = (p1, . . . , pn) are a subset of the free...
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We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1952
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1952-0047071-2