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1Mathematics Department, San Francisco State University, San Francisco, CA 94132, USA. E-mail: robbins@math.sfsu.edu
Citation Information: Georgian Mathematical Journal. Volume 13, Issue 4, Pages 783–786, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2006.783, March 2010
Let , 𝑘 be integers such that 0 < < 𝑘 and (, 𝑘) = 1. If 1 ≤ 𝑖 ≤ 𝑘 – 1, let 𝑟𝑖 be the least positive residue (mod 𝑘) of 𝑖. Let the permutation
For 1 ≤ 𝑖 < 𝑗 ≤ 𝑘 – 1, if 𝑟𝑖 > 𝑟𝑗, this is called an inversion of σ , 𝑘. Let 𝐼(, 𝑘) denote the total number of inversions of σ , 𝑘. In this note, we prove several identities concerning 𝐼(, 𝑘).
Key words and phrases:: Inversions; Dedeking sums
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