Displaying similar documents to “On invariants of certain proper isomorphism classes of (μ, Δ, y)-systems”

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

Similarity:

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.

Link invariants from finite racks

Sam Nelson (2014)

Fundamenta Mathematicae

Similarity:

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

Similarity:

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∗ ⋯...

An analytical approach to Cayley-Hamilton theorem

Luiz C. Martins (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.

An analytical approach to Cayley-Hamilton theorem

Luiz C. Martins (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.