Bruhat intervals as rooks on skew Ferrers boards (2006)
We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It...
Cylindrical lattice paths and the Loehr-Warrington 10^n conjecture (2005)
The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger: There are 10^n zero-sum words of length 5n in the alphabet {+3,-2} such that...
On the sign-imbalance of skew partition shapes (2005)
Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the...
Expected number of inversions after a sequence of random adjacent transpositions (2004)
Eriksson, Henrik, Eriksson, Kimmo, Sjostrand, Jonas
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 these rearrangement...
Exact expectations for random graphs and assignments (2004)
Eriksson, Henrik, Eriksson, Kimmo, Sjostrand, Jonas
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 the expected...
Note on the lamp lighting problem (2004)
Eriksson, Henrik, Eriksson, Kimmo, Sjostrand, Jonas
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 with an edge...
Optimal stopping in a two-sided secretary problem (2004)
Eriksson, Kimmo, Sjostrand, Jonas, Strimling, Pontus
In the "secretary problem", well-known in the theory of optimal stopping, an employer is about to interview a maximum of N secretaries about which she has no prior information. Chow et al. proved...
Conjectures on three-dimensional stable matching (2004)
Eriksson, Kimmo, Sjostrand, Jonas, Strimling, Pontus
We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on...
The cover pebbling theorem (2004)
For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty...