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6 papers · 1 filter
Restricted completion of sparse partial Latin squares
Lina J. Andrén, Carl Johan Casselgren, Klas Markström
An partial Latin square is called -dense if each row and column has at most non-empty cells and each symbol occurs at most times in . An $n \times…
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…
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
Axel Hultman, Svante Linusson, John Shareshian +1
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation $w\in \Sn$ is at most the number of ele…
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…