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View article: Pattern Avoiding Permutations Enumerated by Inversions
Pattern Avoiding Permutations Enumerated by Inversions Open
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simio…
View article: Restricted Permutations Enumerated by Inversions
Restricted Permutations Enumerated by Inversions Open
Permutations are usually enumerated by size, but new results can be found by\nenumerating them by inversions instead, in which case one must restrict one's\nattention to indecomposable permutations. In the style of the seminal paper by\nSi…
View article: Permutations with Few Inversions
Permutations with Few Inversions Open
A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C…
View article: Permutations with few inversions
Permutations with few inversions Open
A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C…
View article: The difficulty of beating the Taxman
The difficulty of beating the Taxman Open
The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular ki…
View article: Counting tournament score sequences
Counting tournament score sequences Open
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…