Displaying similar documents to “Inverse zero-sum problems and algebraic invariants”

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

Algebraic classification of the Weyl tensor: selected applications

Pravda, Vojtěch

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Selected applications of the algebraic classification of tensors on Lorentzian manifolds of arbitrary dimension are discussed. We clarify some aspects of the relationship between invariants of tensors and their algebraic class, discuss generalization of Newman-Penrose and Geroch-Held-Penrose formalisms to arbitrary dimension and study an application of the algebraic classification to the case of quadratic gravity.

Link invariants from finite racks

Sam Nelson (2014)

Fundamenta Mathematicae

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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.

Burnside kei

Maciej Niebrzydowski, Józef H. Przytycki (2006)

Fundamenta Mathematicae

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This paper is motivated by a general question: for which values of k and n is the universal Burnside kei Q̅(k,n) finite? It is known (starting from the work of M. Takasaki (1942)) that Q̅(2,n) is isomorphic to the dihedral quandle Zₙ and Q̅(3,3) is isomorphic to Z₃ ⊕ Z₃. In this paper, we give a description of the algebraic structure for Burnside keis Q̅(4,3) and Q̅(3,4). We also investigate some properties of arbitrary quandles satisfying the universal Burnside relation a = ⋯ a∗b∗ ⋯...

Link invariants from finite biracks

Sam Nelson (2014)

Banach Center Publications

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A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using...