FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2346769286> ?p ?o ?g. }

• W2346769286 endingPage "48" @default.
• W2346769286 startingPage "19" @default.
• W2346769286 abstract "We continue the Coxeter spectral study of the category 𝒰ℬigrm of loop-free edge-bipartite (signed) graphs Δ, with m ≥ 2 vertices, we started in [SIAM J. Discr. Math. 27(2013), 827-854] for corank r = 0 and r = 1. Here we study the class of all non-negative edge-bipartite graphs Δ ∈ 𝒰ℬigrn + r of co rank r ≥ 0, up to a pair of the Gram ℤ-congruences ∼ℤ and ≈ℤ, by means of the non-symmetric Gram matrix GˇΔ∈𝕄n+r(ℤ) of Δ, the symmetric Gram matrix GΔ:=12[GˇΔ+GˇΔtr]∈𝕄n+r(ℤ), the Coxeter matrix CoxΔ:=−GˇΔ⋅GˇΔ−tr∈𝕄n+r(ℤ) and its spectrum speccΔ ⊂ ℂ, called the Coxeter spectrum of Δ. One of the aims in the study of the category 𝒰ℬigrn + r is to classify the equivalence classes of the non-negative edge-bipartite graphs in 𝒰ℬigrn + r with respect to each of the Gram congruences ∼ℤ and ≈ℤ. In particular, the Coxeter spectral analysis question, when the strong congruence Δ≈ℤΔ′ holds (hence also Δ∼ℤΔ′ holds), for a pair of connected non-negative graphs Δ, Δ′ ∈ 𝒰ℬigrn + r such that speccΔ = speccΔ′, is studied in the paper. One of our main aims is an algorithmic description of a matrix B defining the Gram ℤ-congruences Δ≈ℤΔ′ and Δ∼ℤΔ′ , that is, a ℤ-invertible matrix B∈𝕄n+r(ℤ) such that GˇΔ′=Btr⋅GˇΔ⋅B and GΔ′=Btr⋅GΔ⋅B , respectively. We show that, given a connected non-negative edge-bipartite graph Δ in 𝒰ℬigrn + r of corank r ≥ 0 there exists a simply laced Dynkin diagram D, with n vertices, and a connected canonical r-vertex extension D^:=D^(r) of D of corank r (constructed in Section 2) such that Δ~ℤD^. We also show that every matrix B defining the strong Gram ℤ-congruence Δ≈ℤΔ′ in 𝒰ℬigrn + r has the form B=CΔ⋅B¯⋅CΔ′−1, where CΔ,CΔ′∈Mn+r(ℤ) are fixed ℤ-invertible matrices defining the weak Gram congruences Δ~ℤD^ and Δ′~ℤD^ with an r-vertex extended graph D^, respectively, and B¯∈𝕄n+r(ℤ) is ℤ-invertible matrix lying in the isotropy group G1(n+r,ℤ)D^ of D^. Moreover, each of the columns k∈ℤn+r of B is a root of ℤ, i.e., k⋅GˇΔ⋅ktr=1. Algorithms constructing the set of all such matrices B are presented in case when r = 0. We essentially use our construction of a morsification reduction map ϕD^:UBigrD^→MorD^ that reduces (up to ≈ℤ) the study of the set 𝒰ℬigrD^ of all connected non-negative edge-bipartite graphs Δ in 𝒰ℬigrn + r such that Δ~ℤD^ to the study of G1(n+r,ℤ)D^-orbits in the set MorD^⊆G1(n+r,ℤ) of all matrix morsifications of the graph D^." @default.
• W2346769286 created "2016-06-24" @default.
• W2346769286 creator A5008584401 @default.
• W2346769286 date "2016-05-03" @default.
• W2346769286 modified "2023-10-16" @default.
• W2346769286 title "Symbolic Algorithms Computing Gram Congruences in the Coxeter Spectral Classification of Edge-bipartite Graphs, I. A Gram Classification" @default.
• W2346769286 cites W1010616232 @default.
• W2346769286 cites W108936587 @default.
• W2346769286 cites W1261728726 @default.
• W2346769286 cites W141699115 @default.
• W2346769286 cites W1480516528 @default.
• W2346769286 cites W1484273426 @default.
• W2346769286 cites W1553753142 @default.
• W2346769286 cites W1565930783 @default.
• W2346769286 cites W1601437069 @default.
• W2346769286 cites W1633885552 @default.
• W2346769286 cites W1644217377 @default.
• W2346769286 cites W1661437722 @default.
• W2346769286 cites W1917991439 @default.
• W2346769286 cites W1933165643 @default.
• W2346769286 cites W1966056208 @default.
• W2346769286 cites W1976264037 @default.
• W2346769286 cites W1977773351 @default.
• W2346769286 cites W1985968422 @default.
• W2346769286 cites W1987885619 @default.
• W2346769286 cites W1989125084 @default.
• W2346769286 cites W1999102455 @default.
• W2346769286 cites W2005212040 @default.
• W2346769286 cites W2014289472 @default.
• W2346769286 cites W2016582619 @default.
• W2346769286 cites W2016930771 @default.
• W2346769286 cites W2017014095 @default.
• W2346769286 cites W2021515518 @default.
• W2346769286 cites W2024955032 @default.
• W2346769286 cites W2028449252 @default.
• W2346769286 cites W2028618202 @default.
• W2346769286 cites W2032248635 @default.
• W2346769286 cites W2033229665 @default.
• W2346769286 cites W2039997285 @default.
• W2346769286 cites W2041662948 @default.
• W2346769286 cites W2046345195 @default.
• W2346769286 cites W2061472895 @default.
• W2346769286 cites W2066818605 @default.
• W2346769286 cites W2069093337 @default.
• W2346769286 cites W2071227896 @default.
• W2346769286 cites W2080860082 @default.
• W2346769286 cites W2083987881 @default.
• W2346769286 cites W2093802232 @default.
• W2346769286 cites W2197491934 @default.
• W2346769286 cites W2304308747 @default.
• W2346769286 cites W2313352869 @default.
• W2346769286 cites W2330543652 @default.
• W2346769286 cites W2345501689 @default.
• W2346769286 cites W2503589681 @default.
• W2346769286 cites W2519096471 @default.
• W2346769286 cites W2604988676 @default.
• W2346769286 cites W287771455 @default.
• W2346769286 cites W393416684 @default.
• W2346769286 cites W593236292 @default.
• W2346769286 cites W934221954 @default.
• W2346769286 cites W965483201 @default.
• W2346769286 cites W1649048995 @default.
• W2346769286 cites W1763439514 @default.
• W2346769286 doi "https://doi.org/10.3233/fi-2016-1345" @default.
• W2346769286 hasPublicationYear "2016" @default.
• W2346769286 type Work @default.
• W2346769286 sameAs 2346769286 @default.
• W2346769286 citedByCount "18" @default.
• W2346769286 countsByYear W23467692862016 @default.
• W2346769286 countsByYear W23467692862017 @default.
• W2346769286 countsByYear W23467692862019 @default.
• W2346769286 countsByYear W23467692862020 @default.
• W2346769286 countsByYear W23467692862021 @default.
• W2346769286 countsByYear W23467692862022 @default.
• W2346769286 countsByYear W23467692862023 @default.
• W2346769286 crossrefType "journal-article" @default.
• W2346769286 hasAuthorship W2346769286A5008584401 @default.
• W2346769286 hasConcept C114614502 @default.
• W2346769286 hasConcept C118615104 @default.
• W2346769286 hasConcept C121332964 @default.
• W2346769286 hasConcept C132525143 @default.
• W2346769286 hasConcept C140860697 @default.
• W2346769286 hasConcept C143669375 @default.
• W2346769286 hasConcept C158693339 @default.
• W2346769286 hasConcept C197657726 @default.
• W2346769286 hasConcept C33923547 @default.
• W2346769286 hasConcept C62520636 @default.
• W2346769286 hasConcept C77246614 @default.
• W2346769286 hasConcept C80899671 @default.
• W2346769286 hasConcept C9973445 @default.
• W2346769286 hasConceptScore W2346769286C114614502 @default.
• W2346769286 hasConceptScore W2346769286C118615104 @default.
• W2346769286 hasConceptScore W2346769286C121332964 @default.
• W2346769286 hasConceptScore W2346769286C132525143 @default.
• W2346769286 hasConceptScore W2346769286C140860697 @default.
• W2346769286 hasConceptScore W2346769286C143669375 @default.
• W2346769286 hasConceptScore W2346769286C158693339 @default.
• W2346769286 hasConceptScore W2346769286C197657726 @default.

• next