4 papers
Containing all permutations
Michael Engen, Vincent Vatter
Numerous versions of the question "what is the shortest object containing all permutations of a given length?" have been asked over the past fifty years: by Karp (via Knuth) in 197…
Stack-Sorting, Set Partitions, and Lassalle's Sequence
Colin Defant, Michael Engen, Jordan A. Miller
We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to s…
Universal layered permutations
Michael Albert, Michael Engen, Jay Pantone +1
We establish an exact formula for the length of the shortest permutation containing all layered permutations of length , proving a conjecture of Gray.
On the dimension of downsets of integer partitions and compositions
Michael Engen, Vincent Vatter
We characterize the downsets of integer partitions (ordered by containment of Ferrers diagrams) and compositions (ordered by the generalized subword order) which have finite dimens…