In this paper, new variations of some well-known permutation statistics are introduced and studied. Firstly, a double-descent of a permutation π is defined as a position i where πi ≥ 2πi+1. By proofs by induction and direct proofs, recursive and explicit expressions for the number of n-permutations with k double-descents are presented. Also, an expression for the total number of double-descents in all n-permutations is presented. Secondly, a double-inversion of a permutation π is defined as a pair (πi,πj) where i<j but πi ≥ 2πj. The total number of double-inversions in all n-permutations is presented.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-54431 |
| Date | January 2021 |
| Creators | Boberg, Jonas |
| Publisher | Mälardalens högskola, Akademin för utbildning, kultur och kommunikation |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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