Sets with a negative number of elements

Gamma is a programming model where computation is seen as chemical reactions between data represented as molecules floating in a chemical solution. Formally, this model is represented by the rewriting of a multiset where rewrite rules model the chemical reactions. Recently, we have proposed the γ-calculus, a higher-order extension, where the rewrite rules are first-class citizen. The work presented in this paper increases further the expressivity of the chemical model with generalized multisets: multiplicities of elements may be infinite and/or negative. Applications of these new notions are illustrated by some programming examples.

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“…Hybrid multisets [7,10] are a generalization of multisets. In a hybrid multiset, the multiplicity of an element can be negative.…”

Section: Negative Multiplicitiesmentioning

confidence: 99%

“…Grammar 2 gives its syntax.J.-P.Banâtre et al / Electronic Notes in Theoretical Computer Science 135 (2006) [3][4][5][6][7][8][9][10][11][12][13] …”

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confidence: 99%

A Generalized Higher-Order Chemical Computation Model

Banâtre

Fradet

Radenac

2006

Electronic Notes in Theoretical Computer Science

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“…Definition 1 (D. Loeb [11]) Given a universe U , any function f : U → Z is called a hybrid set. The value of f (x) is said to be the multiplicity of the element x.…”

Section: Preliminariesmentioning

confidence: 99%

A New Shuffle Convolution for Multiple Zeta Values

Yee

2005

J Algebr Comb

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“…Also we recall that when qm(x) = xm, we have the classical formula This duality can be interpreted by using the concept of hybrid set introduced by Loeb [6].…”

Section: Generalized Lah Numbersmentioning

confidence: 99%

On the Connection Constants

1991

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We derive explicit formulas for the connection constants between sequences of polynomials in terms of their roots. As an application, we give some properties about the inversion of triangular matrices. By means of the concept of punctured partition of an integer, here introduced to compute connection constants, we also obtain a new expression of the relationship between elementary and complete homogeneous symmetric functions.

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Sets with a negative number of elements

Cited by 35 publications

References 4 publications

A Generalized Higher-Order Chemical Computation Model

A Generalized Higher-Order Chemical Computation Model

A New Shuffle Convolution for Multiple Zeta Values

On the Connection Constants

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