Results 11 to 20 of about 1,238,875 (302)

A Note on Brill–Noether Theory and Rank-Determining Sets for Metric Graphs [PDF]

International Mathematics Research Notices, 2012
We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs also have minimal rank determining sets that are larger than expected, giving couterexamples to a conjecture of Luo.
Chang Mou Lim, Sam Payne, Natasha Potashnik   +2 more
openalex   +4 more sources

Dilation Theory for Rank 2 Graph Algebras

, 2007
29 pages, 5 ...
Kenneth R. Davidson, S. C. Power, Dilian Yang   +2 more
openalex   +4 more sources

Wavelets and graph $C^*$-algebras [PDF]

arXiv, 2016
Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask.
A. Jonsson, A. Kumjian, A. Kumjian, A. Kumjian, A. Kumjian, A. Kumjian, A. Sims, A. Sims, A. Skalski, C. Farsi, C. Farthing, D. Dutkay, D. Hammond, D. Hammond, D. Pask, D. Pask, D. Pask, D. Pask, D. Pask, D.E. Dutkay, D.E. Dutkay, D.G. Evans, D.I. Robertson, D.I. Robertson, D.W. Kribs, F.K. Chung, G. Robertson, G. Robertson, I. Raeburn, J. Spielberg, J.E. Hutchinson, K.R. Davidson, K.R. Davidson, M. Marcolli, N. Brownlowe, O. Bratteli, R. Strichartz, S. Mallat, S. Power, T. Carlsen   +39 more
core   +2 more sources

Graph Spectral Properties of Deterministic Finite Automata [PDF]

arXiv, 2014
We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of
A. Goldberg, A. Nerode, C. Choffrut, J. Sakarovitch, P.V. Mieghem, S.M. Osnaga   +5 more
core   +2 more sources

On the K-theory of higher rank graph C*-algebras

, 2004
Given a row-finite $k$-graph $ $ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*( )$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of $C^*( )$. The $K$-groups of $C^*( )$ for $k>2$ can be calculated under certain circumstances and we consider the case $k=3$. We prove that
D. Gwion Evans
openalex   +4 more sources

The K-theory of the C*-algebras of 2-rank graphs associated to complete bipartite graphs

, 2021
Using a result of Vdovina, we may associate to each complete connected bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $\kappa$.
Mutter, S. A.
core   +3 more sources

Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions [PDF]

, 2017
Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement.
Hogben, L, Palmowski, KF, Roberson, DE, Severini, S   +3 more
core   +2 more sources

An intuitionistic fuzzy graph’s variation coefficient measure with application to selecting a reliable alliance partner [PDF]

Scientific Reports
Group decision-making (GDM) is crucial in various components of graph theory, management science, and operations research. In particular, in an intuitionistic fuzzy group decision-making problem, the experts communicate their preferences using ...
Naveen Kumar Akula, Sharief Basha S, Nainaru Tarakaramu, Obbu Ramesh, Sameh Askar, Uma Maheswari Rayudu, Hijaz Ahmad, M. Ijaz Khan   +7 more
doaj   +2 more sources

The Rank-Ramsey Problem and the Log-Rank Conjecture [PDF]

arXiv
A graph is called Rank-Ramsey if (i) Its clique number is small, and (ii) The adjacency matrix of its complement has small rank. We initiate a systematic study of such graphs. Our main motivation is that their constructions, as well as proofs of their non-existence, are intimately related to the famous log-rank conjecture from the field of ...
Gal Beniamini, N. Linial, Adi Shraibman
arxiv   +2 more sources

Dilation theory for rank two graph algebras.

, 2010
An analysis is given of $*$-representations of rank 2 single vertex graphs. We develop dilation theory for the non-selfadjoint algebras $\A_\theta$ and $\A_u$ which are associated with the commutation relation permutation $\theta$ of a 2-graph and, more generally, with commutation relations determined by a unitary matrix $u$ in $M_m(\bC) \otimes M_n ...
Kenneth R. Davidson, S. C. Power, Dilian Yang   +2 more
openalex   +2 more sources