Matches in SemOpenAlex for { <https://semopenalex.org/work/W2136619024> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W2136619024 endingPage "281" @default.
- W2136619024 startingPage "269" @default.
- W2136619024 abstract "Consider S n , the symmetric group on n letters, and let maj π denote the major index of π ∈ S n . Given positive integers k , l and nonnegative integers i , j , define m n k , l ( i , j ) : = # { π ∈ S n : maj π ≡ i ( mod k ) and maj π −1 ≡ j ( mod l ) } . We give a bijective proof of the following result which had been previously proven by algebraic methods: If k , l are relatively prime and at most n then m n k , l ( i , j ) = n ! k l which, surprisingly, does not depend on i and j . Equivalently, if m n k , l ( i , j ) is interpreted as the ( i , j ) -entry of a matrix m n k , l , then this is a constant matrix under the stated conditions. This bijection is extended to show the more general result that, for d ⩾ 1 and k , l relatively prime, the matrix m n k d , l d admits a block decomposition where each block is the matrix m n d , d / ( k l ) . We also give an explicit formula for m n n , n , and show that if p is prime then m n p p , p has a simple block decomposition. To prove these results, we use the representation theory of the symmetric group and certain restricted shuffles." @default.
- W2136619024 created "2016-06-24" @default.
- W2136619024 creator A5050021092 @default.
- W2136619024 creator A5070369805 @default.
- W2136619024 creator A5072366611 @default.
- W2136619024 date "2007-08-01" @default.
- W2136619024 modified "2023-10-18" @default.
- W2136619024 title "Counting permutations by congruence class of major index" @default.
- W2136619024 cites W2031359422 @default.
- W2136619024 cites W2065273766 @default.
- W2136619024 cites W2109216294 @default.
- W2136619024 cites W2145596344 @default.
- W2136619024 cites W2495029002 @default.
- W2136619024 cites W2914659449 @default.
- W2136619024 doi "https://doi.org/10.1016/j.aam.2006.03.002" @default.
- W2136619024 hasPublicationYear "2007" @default.
- W2136619024 type Work @default.
- W2136619024 sameAs 2136619024 @default.
- W2136619024 citedByCount "1" @default.
- W2136619024 crossrefType "journal-article" @default.
- W2136619024 hasAuthorship W2136619024A5050021092 @default.
- W2136619024 hasAuthorship W2136619024A5070369805 @default.
- W2136619024 hasAuthorship W2136619024A5072366611 @default.
- W2136619024 hasBestOaLocation W21366190241 @default.
- W2136619024 hasConcept C114614502 @default.
- W2136619024 hasConcept C118615104 @default.
- W2136619024 hasConcept C132074034 @default.
- W2136619024 hasConcept C136764020 @default.
- W2136619024 hasConcept C154945302 @default.
- W2136619024 hasConcept C2524010 @default.
- W2136619024 hasConcept C2777212361 @default.
- W2136619024 hasConcept C2777382242 @default.
- W2136619024 hasConcept C33923547 @default.
- W2136619024 hasConcept C41008148 @default.
- W2136619024 hasConceptScore W2136619024C114614502 @default.
- W2136619024 hasConceptScore W2136619024C118615104 @default.
- W2136619024 hasConceptScore W2136619024C132074034 @default.
- W2136619024 hasConceptScore W2136619024C136764020 @default.
- W2136619024 hasConceptScore W2136619024C154945302 @default.
- W2136619024 hasConceptScore W2136619024C2524010 @default.
- W2136619024 hasConceptScore W2136619024C2777212361 @default.
- W2136619024 hasConceptScore W2136619024C2777382242 @default.
- W2136619024 hasConceptScore W2136619024C33923547 @default.
- W2136619024 hasConceptScore W2136619024C41008148 @default.
- W2136619024 hasIssue "2" @default.
- W2136619024 hasLocation W21366190241 @default.
- W2136619024 hasLocation W21366190242 @default.
- W2136619024 hasLocation W21366190243 @default.
- W2136619024 hasOpenAccess W2136619024 @default.
- W2136619024 hasPrimaryLocation W21366190241 @default.
- W2136619024 hasRelatedWork W1978042415 @default.
- W2136619024 hasRelatedWork W2010885377 @default.
- W2136619024 hasRelatedWork W2017331178 @default.
- W2136619024 hasRelatedWork W2054351634 @default.
- W2136619024 hasRelatedWork W2271889716 @default.
- W2136619024 hasRelatedWork W2315540400 @default.
- W2136619024 hasRelatedWork W2962776692 @default.
- W2136619024 hasRelatedWork W2976797620 @default.
- W2136619024 hasRelatedWork W3086542228 @default.
- W2136619024 hasRelatedWork W4240363806 @default.
- W2136619024 hasVolume "39" @default.
- W2136619024 isParatext "false" @default.
- W2136619024 isRetracted "false" @default.
- W2136619024 magId "2136619024" @default.
- W2136619024 workType "article" @default.