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Problem 4: An inversion in a permutation T = T1... Tn (written in one-line notation) is a pair of indices 1 pinv(7) (1+x)(1+x+ x²)..· (1 +x + x² +……+x"-1), n-. TES. where x is a variable.

Problem 4: An inversion in a permutation T = T1... Tn (written in one-line notation) is a pair of indices 1 pinv(7) (1+x)(1+x+ x²)..· (1 +x + x² +……+x"-1), n-. TES. where x is a variable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 4: An inversion in a permutation T = T1 . .. Tn (written in one-line notation) is a pair of indices 1 < i <j <n which appear out-of-order when we read a from left to right. For example, if T = inv(T) denote the number of inversions in T, so that inv(7) = 4 in our example. Prove that 23514, the inversions in T are 12,13, 15, and 45. Let prinv(#) = .. (1+x + x² + ...+ x"-1), (1+ x)(1+x+ x²) TESN where x is a variable.
Transcribed Image Text:Problem 4: An inversion in a permutation T = T1 . .. Tn (written in one-line notation) is a pair of indices 1 < i <j <n which appear out-of-order when we read a from left to right. For example, if T = inv(T) denote the number of inversions in T, so that inv(7) = 4 in our example. Prove that 23514, the inversions in T are 12,13, 15, and 45. Let prinv(#) = .. (1+x + x² + ...+ x"-1), (1+ x)(1+x+ x²) TESN where x is a variable.
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