Index
(C•)α, 9
C•, 1, 7
Nd-graded
complex, 9
MinGen(in≺(a)), 13
Path(c, c ), 8
m(w), 12
acyclic matching, 2, 7
infinite, 9
algebra
associative, 29
Cohen-Macaulay, 43
differential graded, 18
exterior, 31, 33
Koszul, 17, 25
semigroup, 25
alphabet, 15
Anick resolution, 11, 14, 17, 21, 23
bimodule, 30
binomial, 25
Cartan complex, 26
cellular chain complex, 8, 36
chain complex, 1, 7
cellular, 8, 36
complete intersection, 18, 29, 32
complex
Nn-graded, 9
multigraded, 9
critical vertex, 8
CW-complex, 35
P -graded, 35
regular, 37
cycle
directed, 2, 7
deterministic finite automaton, 24
DFA, 24
differential, 7
differential graded algebra, 18
directed
cycle, 2, 7
edge, 1
path, 2
weighted graph, 1, 7
discrete Morse theory, 1, 2, 7
algebraic, 1, 2, 8
edge
weight, 1, 7
exterior algebra, 31, 33
f-vector, 36
free module, 7
fully attached, 14, 15, 23, 24, 30
Gr¨obner
basis, 11
infinite, 27
non.commutative, 21
quadratic, 17, 21, 25
reduced, 11, 18, 31
representation, 15, 21
graph
directed weighted, 7
Hilbert series, 25, 32
Hochschild complex, 29, 58
Hochschild homology, 29
ideal, 11
Borel fixed, 35, 37
complete intersection, 18
generic initial, 37, 40
initial, 11
monomial, 37
non-commutative lattice, 21
p-Borel fixed, 35, 54
principal Borel fixed, 37
principal Cohen-Macaulay p-Borel fixed,
49
principal p-Borel fixed, 41
two-sided, 21, 30
initial ideal, 11
Koszul algebra, 17, 25
Koszul complex, 26
language, 15, 17
regular, 25
73
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