Wyniki wyszukiwania - Biblioteka Nauki

Ten serwis zostanie wyłączony 2025-02-11.

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

1 Fundamenta Informaticae

1 2015

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Algorithms for Isotropy Groups of Cox-regular Edge-bipartite Graphs

100%

Kasjan S. , Simson D.

tom Vol. 139, nr 3

249--275

This paper can be viewed as a third part of our paper [Fund. Inform. 2015, in press]. Following our Coxeter spectral study in [Fund. Inform. 123(2013), 447-490] and [SIAM J. Discr. Math. 27(2013), 827-854] of the category UBigrn of loop-free edge-bipartite (signed) graphs Δ, with n ≥ 2 vertices, we study a larger category RBigrn of Cox-regular edge-bipartite graphs Δ (possibly with dotted loops), up to the usual Z-congruences ~Z and ≈Z. The positive graphs Δ in RBigrn, with dotted loops, are studied by means of the complex Coxeter spectrum speccΔ ⊂ C, the irreduciblemesh root systems of Dynkin types Bn, n ≥ 2, Cn, n ≥ 3, F4, G2, the isotropy group G1(n, Z)Δ (containing the Weyl group of Δ), and by applying the matrix morsification technique introduced in [J. Pure Appl. Algebra 215(2011), 13-24]. Here we present combinatorial algorithms for constructing the isotropy groups G1(n,Z)Δ. One of the aims of our three paper series is to develop computational tools for the study of the Zcongruence ~Z and the following Coxeter spectral analysis question: "Does the congruence Δ ≈Z Δ' holds, for any pair of connected positive graphsΔ,Δ' ∈ RBigrn such that speccΔ = speccΔ' and the numbers of loops in Δ and Δ' coincide?". For this purpose, we construct in this paper a extended inflation algorithm Δ → DΔ, with DΔ ~Z Δ, that allows a reduction of the question to the Coxeter spectral study of the G1(n,Z)D-orbits in the set MorD ⊂ Mn(Z) of matrix morsifications of the associated edge-bipartite Dynkin graph D = DΔ ∈ RBigrn. We also outline a construction of a numeric algorithm for computing the isotropy group G1(n,Z)Δ of any connected positive edge-bipartite graph Δ in RBigrn. Finally, we compute the finite isotropy group G1(n,Z)D, for each of the Cox-regular edge-bipartite Dynkin graphs D.