Symmetric polynomials in tropical algebra semirings
Reads0
Chats0
TLDR
This paper identifies in which of these upper-bound semirings in tropical algebra the authors can express symmetric polynomials in terms of elementary ones and shows that in the case of idempotentSemirings this is always possible, and that in non-trivial symmetrized semiring this is never possible.About:
This article is published in Journal of Symbolic Computation.The article was published on 2019-07-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Kleene algebra & Ring of symmetric functions.read more
Citations
More filters
Posted Content
Tropical time series, iterated-sums signatures and quasisymmetric functions
TL;DR: This work introduces the iterated-sums signature over any commutative semiring, as it leads to features of real-valued time series that are not easily available using existing signature-type objects.
Journal ArticleDOI
Symmetric polynomials in upper-bound semirings
Sara Kališnik,Davorin Lešnik +1 more
TL;DR: The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is elementary, i.e. every polynomial over a ring can be expressed with elementary upper-bound semirings in a unique way as mentioned in this paper.
Book
Mathematical foundations of computer science 1988 : proceedings of the 13th Symposium, Carlsbad, Czechoslovakia, August 29-September 2, 1988
TL;DR: Design, proof and analysis of new efficient algorithms for incremental attribute evaluation and a decomposition theorem for finite-valued transducers and an application to the equivalence problem.
Posted Content
Symmetric Polynomials in Upper-bound Semirings
Sara Kališnik,Davorin Lešnik +1 more
TL;DR: This paper extends the known results and gives a complete characterization of fully elementary upper-bound semirings and improves this characterization statement in the case of linearly ordered upper- bound semiring.
Journal ArticleDOI
Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions
TL;DR: In this paper , the iterated-sums signature over arbitrary commutative semirings is proposed to extract features of realvalued time series that are not easily available using existing signature-type objects.
References
More filters
Book
Semirings and their Applications
TL;DR: In this paper, the authors define Hemirings and semirings as "sets and relations with values with values in a semiring" and define a set of conditions on semimodal construction.
Book
Introduction to Tropical Geometry
Diane Maclagan,Bernd Sturmfels +1 more
TL;DR: Tropical islands Building blocks Tropical varieties Tropical rain forest Tropical garden Toric connections Bibliography Index Bibliography as mentioned in this paper, Section 5.1.1] and Bibliography 2.2.
Book
Max-linear Systems: Theory and Algorithms
TL;DR: Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max- algebraic Subspaces.
Dissertation
Theorie des systemes lineaires dans les dioides
TL;DR: In this paper, the systemes d'equations lineaires dans certains dioides, for lesquels on retrouve l'analogue de la theorie de cramer a condition de se placer dans un dioide symetrise, adapte les algorithmes iteratifs usuels (jacobi, gauss-seidel).
Book ChapterDOI
Methods and Applications of (MAX, +) Linear Algebra
Stéphane Gaubert,Max Plus +1 more
TL;DR: Exotic semirings have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, Hamilton-Jacobi theory; asymptotic analysis.