Henrik Eriksson

KTH Royal Institute of Technology | KTH · School of Computer Science and Communication (CSC)

A multipermutation with $k$ copies each of $1\ldots n$ is Carlitz if neighbours are different. We enumerate these objects for $k=2,3,4$ and derive recurrences. In particular, we prove and improve a conjectured recurrence for $k=3$, stated in OEIS, the Online Encyclopedia of Integer Sequences.

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 to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rot...

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 neighbours. For a Coxeter graph, words represent group elements. D. E. Speyer recently proved that words with the intervening neighbours property are reduced if the group is in...

We study the length L k of the shortest permutation containing all patterns of length k. We establish the bounds e −2k 2 < L k ≤ (2/3 + o(1))k 2. We also prove that as k → ∞, there are permutations of length (1/4 + o(1))k 2 containing almost all patterns of length k.

In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of ap-plications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive inte-gers to a theorem of MacMahon and mock theta functions is explore...

We give expressions for the expected number of inversions after t random adjacent transpositions have been performed on the identity permutation in S n + 1 The problem is a simplification of a problem motivated by genome evolution. For a fixed t and for all n ≥ t, the expected number of inversions after t random adjacent transpositions is $${E_{nt}...

We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer11 (1989), 49–53]. 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 directed to the lamp. For example, we show that every configuration of lamp...

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 length of the corresponding minimal spanning forest. For a random bipartite graph we give a formula for the expected time at which a k-assignment appears. T...

Abstract Sorting a permutation by block moves is a task that every bridge player has to solve every time she picks up a new hand of cards. It is also a problem for the computational biologist, for block moves are a fundamental type of mutation that can explain why genes common,to two species do not occur in the same order in the chromosome. It is n...

Measurements of differences in optical path length in monochromatic light with any interferometric method are insensitive to errors that are a whole number of waves. If measurements are performed in several wavelengths, this ambiguity can be resolved. We present a general algorithm for finding the correct distance post facto, given multiple measure...

Wavefront sensing in monochromatic light is insensitive to segment piston errors that are a whole number of waves. If the wavefront sensing is performed in several wavelengths, this ambiguity can be resolved. We give an algorithm for finding the correct phase, given multiple measurements in different wavelengths. Using this algorithm, the capture r...

We introduce color-signed permutations to obtain a very explicit com- binatorial interpretation of the q-Eulerian identities of Brenti and some generaliza- tions. In particular, we prove an identity involving the golden ratio, which allows us to compute upper bounds on how high a checker can reach in a classical checker- jumping problem, when the r...

We present a unified theory for permutation models of all the infinite families of finite and a#ne Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott&apos;s formula (in the refined version of Macdonald) for the Poincareseriesofthese a#ne Weyl groups. 1991 Mathematics Subje...

We determine the maximum area of a rectangular food trolley that can be pushed around a corner. We also discuss various pushing strategies.

The analysis of chessboard pebbling by Fan Chung, Ron Graham, John Morrison and Andrew Odlyzko is strengthened and generalized, first to higher dimension and then to arbitrary posets. Subject Classification: Primary 05A15; secondary 05E99. 1 The pebbling game The pebbling game of Kontsevich is played on the grid points of the first quadrant. One st...

We consider a generalization of an old checker jumping problem from d = 2 to d ⩾ 2: What is the maximum of xd if it is possible to bring a checker to the point (x1, x2, … xd) in Zd, starting with a distribution of checkers at lattice-points in the half-space xd ⩽ 0? We prove that the answer is 3d − 2. The next question is as follows: Bringing two c...