Papers by Henrik Eriksson
International Journal of Mathematical Education in Science and Technology, 1985
ABSTRACT
Applied Scientific Research, 1986
One of the best methods for seasonal storage of solar heat is the storage of hot water in large u... more One of the best methods for seasonal storage of solar heat is the storage of hot water in large unlined rock caverns. A safe method to build self stabilizing very large caverns is to excavate them partially, i.e. to leave a considerable amount of the blasted rock in the cavern.
UV, Optical, and IR Space Telescopes and Instruments, 2000
Wavefront sensing in monochromatic light is insensitive to segment piston errors that are a whole... more 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 range of a wavefront sensor can be extended from on the order of ¢ ¡ ¤ £ 2 in piston to several waves. This relaxes the demands on an initial, coarse alignment method. The extended capture range depends on the selection of wavelengths available for phase measurements and the expected accuracy of the wavefront sensing method used.
The electronic journal of combinatorics
Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours prope... more 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 infinite and irreducible [Proc. Am. Math. Soc. 137, No. 4, 1295-1302 (2009; Zbl 1187.20053)]. We present a new and shorter proof using the root automaton for recognition of reduced words.
The electronic journal of combinatorics
We present a unified theory for permutation models of all the infinite families of finite and a#n... more 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's formula (in the refined version of Macdonald) for the Poincareseriesofthese a#ne Weyl groups. 1991 Mathematics Subject Classification. primary 20B35; secondary 05A15. 1 Introduction The aim of this paper is to present a unified theory for permutation representations of the finite Weyl groups A n-1 , B n , C n , D n , and the a#ne Weyl groups # A n-1 , # B n , # C n , # D n . Our starting point is the symmetric group S n , the group of permutations of [1,...,n]. If S n is presented as the group generated by adjacent transpositions, it is isomorphic to the Weyl group A n-1 , and we obtain well-known interpretations of several Coxeter group concepts in permutation language: 1. The Coxeter generators are the adjacent transpositions. 2. Reflections corresp...
For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group ele... more 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 rotations and legal commutations.
Optical Engineering, 2001
Measurements of differences in optical path length in monochromatic light with any interferometri... more 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 measurements in different wavelengths. Applied e.g. to piston measurements of a segmented mirror, the capture range of a wavefront sensor can be extended from ¡ half a wave to several waves. The extended capture range can be calculated and depends on the selection of wavelengths used for measurements and on the expected accuracy of the method used.
European Journal of Combinatorics, 1995
We consider a generalization of an old checker jumping problem from d = 2 to d >t 2: What is the ... more We consider a generalization of an old checker jumping problem from d = 2 to d >t 2: What is the maximum of Xd if it is possible to bring a checker to the point (xl, Xz ..... xa) in Z a, starting with a distribution of checkers at lattice-points in the half-space xa <~ 0? We prove that the answer is 3d -2. The next question is as follows: Bringing two checkers to the level 3d -2, what is the minimum distance between them? We prove that the answer is 3. This was not known before, even when d = 2.
Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours prope... more 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. Speyer recently proved that words with the intervening neighbours property are irreducible if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of irreducible words.
We present a uni ed theory for permutation models of all the in nite families of nite and a ne We... more We present a uni ed theory for permutation models of all the in nite families of nite and a ne Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott's formula (in the re ned version of Macdonald) for the Poincar e series of these a ne Weyl groups.
Advances in Applied Mathematics, 2001
The electronic journal of combinatorics
We introduce color-signed permutations to obtain a very explicit com- binatorial interpretation o... more 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 rules are relaxed to allow also diagonal jumps.
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Papers by Henrik Eriksson