Matching Patterns in Strings Subject to Multi Linear Transformations
Matching Patterns in Strings Subject to Multi Linear Transformations
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, Cj, i:, cy2, i, . . . , cy^. Fc satisfy the equation for any pair of locations of the upper and lower patterns of Figure 7 which are J2 — ji apart. ) Proof of corollary 3. 1 Suppose J2 — j\ < rn. By Fact 3. 1, a duel was performed between ji and J2. No one has lost. Each fc-tuple cy, ,1, . . . , Cji, jt in 5y, , is a solution for the system (3. 1). Each k- tuple cy^^i, . . . , cyj_fc in Sj^, is a solution for the system (3. 2). Therefore, for each /, 7^ in witness{J2 — j\ + l) and for each pair of such A;-tuples cy, ,1, . . . , Cj^, jt and Cj^. I, • • •, cyj.^k, we get k k This means that cy, i, . . . , cy, ,jt, cy2, i, . . . , Cj2, fc satisfy each of the equations in 2k unknowns suggested by locations /^ 7^ in wttness{J2 - j\ + 1). The definition of witness{J2 - j\ + 1) implies that these equations span all the equations suggested by any other location. Thus, cy, i, ... , cyj, jfe, cy2, i, ... , cyj, fc also satisfy each of these equations. This establishes Corollary 3.
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To quickly assess the difficulty of the text, read a short excerpt:
, Cj, i:, cy2, i, . . . , cy^. Fc satisfy the equation for any pair of locations of the upper and lower patterns of Figure 7 which are J2 — ji apart. ) Proof of corollary 3. 1 Suppose J2 — j\ < rn. By Fact 3. 1, a duel was performed between ji and J2. No one has lost. Each fc-tuple cy, ,1, . . . , Cji, jt in 5y, , is a solution for the system (3. 1). Each k- tuple cy^^i, . . . , cyj_fc in Sj^, is a solution for the system (3. 2). Therefore, for each /, 7^ in witness{J2 — j\ + l) and for each pair of such A;-tuples cy, ,1, . . . , Cj^, jt and Cj^. I, • • •, cyj.^k, we get k k This means that cy, i, . . . , cy, ,jt, cy2, i, . . . , Cj2, fc satisfy each of the equations in 2k unknowns suggested by locations /^ 7^ in wttness{J2 - j\ + 1). The definition of witness{J2 - j\ + 1) implies that these equations span all the equations suggested by any other location. Thus, cy, i, ... , cyj, jfe, cy2, i, ... , cyj, fc also satisfy each of these equations. This establishes Corollary 3.
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You can find similar books in the "Read Also" column, or choose other free books by T Tzoreff Eliam to read online
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