6 papers
Enumeration of Carlitz Multipermutations
Henrik Eriksson, Alexis Martin
A multipermutation with copies each of is Carlitz if neighbours are different. We enumerate these objects for and derive recurrences. In particular, we pr…
Conjugacy of Coxeter elements
Henrik Eriksson, Kimmo Eriksson
For a Coxeter group (W,S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter…
Words with intervening neighbours in infinite Coxeter groups are reduced
Henrik Eriksson, Kimmo Eriksson
Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighb…
Note on the lamp lighting problem
Henrik Eriksson, Kimmo Eriksson, Jonas Sjostrand
We answer some questions concerning the so called sigma-game of Sutner. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex w…
Exact expectations for random graphs and assignments
Henrik Eriksson, Kimmo Eriksson, Jonas Sjostrand
For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and…
Expected number of inversions after a sequence of random adjacent transpositions
Henrik Eriksson, Kimmo Eriksson, Jonas Sjostrand
In the evolution of a genome, the gene sequence is sometimes rearranged, for example by transposition of two adjacent gene blocks. In biocombinatorics, one tries to reconstruct the…