Of your identical musical form in djanba songs at Wadeye.) As within the aforementioned examples, the cardinality sequence of the cc of subgroups of the group constructed with rel=AABCC corresponds to Isoc( X; two) up to the highest index 9 that we could reach in our calculations.Figure three. Slow movement from Haydn’s `Emperor’ quartet Opus 76, N three.Sci 2021, three,8 ofTable four. Group evaluation of some musical forms whose structure of subgroups, aside from exceptions, is close to Isoc( X; d) with d = two (in the upper a part of the table) or d = 3 (in the reduce a part of the table). Needless to say, the forms A-B-C and A-B-C-D have the cardinality sequence of cc of subgroups specifically equal to Isoc( X; 2) and Isoc( X; 3), respectively. Musical Kind A-B-C-B-A . A-B-A-C-A-B-A A-B-A-C-A, A-B-A-C-A-B-A A-B-A-C A-A-B-C-C . A-A-A-A-B-B-A-A-C-C-A-A . A-A-A-A-B-B-A-A-C-B-A-A . A-A-A-A-B-B-A-A-B-C-A-C . A-B-C . A-A-B-B-C-C-D-D A-B-A-C-A-D-A A-B-C-D . Ref arch, BelBart . . rondo Haydn [32], djanba ([33], Figure 9.8) twelve-bar blues, regular twelve-bar blues, variation 1 twelve-bar blues, variation 2 Isoc( X; 2) . pot pourri rondo Isoc( X; three) . Card. Struct. of cc of Subgr. [1,three,7,26,97,624, 4163,34470,314493] . . . . . [1,7,14,109,396,3347, 19758,287340] [1,3,7,26,97,624, 4163,34470,314493] [1,3,7,26,127, 799, 5168, 42879] [1,three,7,26,97,624, 4163,34470,314493] [1,15,82,1583,30242] [1,7,41,604,13753,504243] [1,7,41,604,13753, 504243,24824785] r two . . . . . . three . two . . . two . four 3 3 .Further musical types with 4 letters A, B, C, and D and their relationship to Isoc( X; three) are provided within the reduced a part of Table four. Not surprisingly, the rank r of your abelian quotient of f p = A, B, C |rel( A, B, C ) is found to become two when the cardinality structure fits that Isoc( X; two) in Table four. Otherwise, the rank is three. Similarly, the rank r in the abelian quotient of f p = A, B, C, D |rel( A, B, C, D ) is identified to be 3 when the cardinality structure fits that Isoc( X; three) in Table four. Otherwise, the rank is four. 5. Graph Coverings for Prose and Poems 5.1. Graph Coverings for Prose Let us perform a group analysis of a lengthy sentence in prose. We selected a text by Charles Baudelaire [34]: Le gamin du c este Empire h ita d’abord; puis, se ravisant, il r ondit: “Je vais vous le dire “. Peu d’instants apr , il reparut, tenant dans ses bras un fort gros chat, et le regardant, comme on dit, dans le blanc des yeux, il affirma sans h iter: “Il n’est pas encore tout fait midi.” Ce qui ait vrai. In Table five, the group analysis is performed with three, four or five letters (in the upper component) and is in comparison to random sequences with the very same quantity of letters (inside the reduce part). The text from the sentence is very first encoded with three letters (H for names and adjectives, E for verbs and C otherwise), we observe that the subgroup structure has cardinality close to that of a totally free group F2 on two letters up to index three. If one adds 1 letter A for the prepositions in the sentence (as well as H, E and C), then the subgroup structure has cardinality close to that of a free of charge group F3 on 3 letters. If adverbs B are also chosen, then the subgroup structure is close to that from the no cost group F4 . In all three cases, the Streptonigrin custom synthesis similarity holds up to index three and that the cc of subgroups are the exact same as in the corresponding cost-free groups. The very first Betti numbers of your producing groups are two, three and four as anticipated. In Table 5, we also BSJ-01-175 Cancer computed the cardinality structure in the cc of subgroups of compact indexes obtained from a random sequence of.