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Burosch, Gustav; Gronau, Hans-Dietrich O. F.; Laborde, Jean-Marie

doi:10.1023/a:1006073600934

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…A similar solution given by John M. Campbell ([6], see [12]) uses only one infinite two-sided sequence (v i ) of consecutive sums (here shown for n = 5)…”

Section: Sums Of Consecutive Elementsmentioning

confidence: 99%

“…Condition (12) guarantees that any negative charge has the option to be distributed among their neighboring vertices. If one admits that c i vanishes for some indices i, it is natural to set all corresponding weights w i j , including w ii , to zero and to modify the procedure by not allowing the substitution (14) for those values of i.…”

Section: Relaxation Proceduresmentioning

confidence: 99%

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Relaxation procedures on graphs

Wegert

Reiher

2009

Discrete Applied Mathematics

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The procedures studied in this paper originate from a problem posed at the International Mathematical Olympiad in 1986. We present several approaches to the IMO problem and its generalizations. In this context we introduce a "signed mean value procedure" and study "relaxation procedures on graphs". We prove that these processes are always finite, thus confirming a conjecture of Akiyama, Hosono and Urabe [J. Akiyama, K. Hosono, M. Urabe, Some combinatorial problems. Discrete Mathematics 116 (1993) 291-298]. Moreover, we indicate relations to sorting and to an iterative method used in circle packing.

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“…A similar solution given by John M. Campbell ([6], see [12]) uses only one infinite two-sided sequence (v i ) of consecutive sums (here shown for n = 5)…”

Section: Sums Of Consecutive Elementsmentioning

confidence: 99%

Section: Relaxation Proceduresmentioning

confidence: 99%

Relaxation procedures on graphs

Wegert

Reiher

2009

Discrete Applied Mathematics

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Computing Orbits of the Automorphism Group of the Subsequence Poset B m,n

Ghorbani

Jalal-Abadi

Ashrafi

2006

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Automorphisms of subword-posets

Ligeti

Sziklai

2005

Discrete Mathematics

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In this paper the automorphism group of two posets, D k,n and B m,n is determined. D k,n is the poset of DNA strands of length at most n, built up with k complement pairs of letters, and partially ordered by the subsequence relation. B m,n is the set of all subsequences of the word u m,n = a 1 ...a n defined over the alphabet {0, 1, ..., (m−1)}, where a i ≡ i (mod m). The automorphism group of B m,n was known already (see Burosch et al. [1]), here a short proof is presented as an illustration of the method used in the first part.

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Cited by 3 publications

References 4 publications

Relaxation procedures on graphs

Relaxation procedures on graphs

Computing Orbits of the Automorphism Group of the Subsequence Poset B m,n

Automorphisms of subword-posets

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