Notation

Abstract

a, b, c Typical symbols from an alphabet 1 A Transposed matrix 39 A > 0 Positive matrix 100 A 0 Nonnegative matrix 100 A B Matrix inequality 100 A > B Strict matrix inequality 100 A≈∼B Elementary equivalence 226 A ≈ B Strong shift equivalence 227 A ∼ B Shift equivalence 235 A Alphabet 1 A k-blocks over A 2 A Full shift over A 2 AG, A(G) Adjacency matrix of graph G 35 AG Symbolic adjacency matrix 65 adjA Adjugate of A 113 B(X) Language of X 9 Bn(X) n-blocks in X 9 βN Higher block map 12 BF (A) Bowen–Franks group 248 BFp(A) Generalized Bowen–Franks group 250 Cf Companion matrix of f 373 Ck(u) Cylinder set using block u 179 χA(t) Characteristic polynomial of A 100 (∆ A ,∆ A , δ A ) Dimension triple of A 252 dφ Degree of sliding block code φ 303 d φ Minimal number of pre-image symbols 304 E(G), E Edge set of graph 33 EI Edges with initial state I 34 E Edges with terminal state J 34 e, f, g Typical edges of a graph 33 〈E〉Q Rational vector space generated by E 397 〈E〉R R-ideal generated by E 417 F Set of forbidden blocks 5 FX(w) Follower set of a word 72 FG(I) Follower set of a state 78 fλ Minimal polynomial of λ 370 fΛ Polynomial associated to list Λ 385 [[φ]] Topological full group 476 (∂Φ, Φ) Graph homomorphism 34 G Graph 33 G Transposed graph 39 G(A), GA Graph with adjacency matrix A 35 G ∼= H Graph isomorphism 34 G[N] Higher edge graph 42 G Higher power graph 45 G= (G,L) Labeled graph 64 GX Minimal presentation of sofic shift 83 G1 ×G2 Product of graphs 87