5 papers · 1 filter
Pattern Avoiding Permutations as Walks
Atli Fannar Franklín
The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: build…
Pattern Avoiding Permutations Enumerated by Inversions
Atli Fannar Franklín
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 indecomposab…
Permutations with few inversions
Anders Claesson, Atli Fannar Franklín, Einar Steingrímsson
A curious generating function for permutations of with exactly inversions is presented. Moreover, is shown to be the generating function for pe…
The difficulty of beating the Taxman
Atli Fannar Franklín, Robert K. Moniot
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…
Counting tournament score sequences
Anders Claesson, Mark Dukes, Atli Fannar Franklín +1
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…