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On a class of partially ordered sets and their linear invariants

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Abstract

Let (ℒ, <) be a finite partially ordered set with rank function. Then ℒ is the disjoint union of the classes ℒ k of elements of rank k and the order relation between elements in ℒ k and ℒ k+1 can be represented by a matrix S k. We study partially ordered sets which satisfy linear recurrence relations of the type S k (S T k ) − c k (S k − 1)T S k − 1 = d + k − c k d − k ) Id for all k and certain coefficients d k +, d k - and c k.

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References

  1. Cameron, P. J., ‘Colour schemes’, Ann. Discrete Math. 15 (1982), 81–95.

    Google Scholar 

  2. Cameron, P. J. and Liebler, R. A., ‘Tactical decompositions and orbits of projective groups’, Linear Algebra Appl. 46 (1982), 91–102.

    Google Scholar 

  3. Cameron, P. J., Neumann, P. Neumann, and Saxl, J., ‘An interchange property for finite permutation groups’, Bull. London Math. Soc. 11 (1979) 161–169.

    Google Scholar 

  4. Camina, A. R. and Siemons, J., ‘Intertwining automorphisms in finite incidence structures’, Linear Algebra Appl. 117 (1989) 25–34.

    Google Scholar 

  5. Dembowski, P., Finite Geometries, Springer-Verlag, 1964.

  6. Higman, D. G., ‘Finite permutation groups of rank 3’, Math. Z. 86 (1964), 145–156.

    Google Scholar 

  7. Livingstone, D. and Wagner, A., ‘Transitivity of finite permutation groups on unordered sets’, Math. Z. 90 (1965), 393–403.

    Google Scholar 

  8. Saxl, J., ‘On points and triples in Steiner triple systems’, Arch. Math. 36 (1981), 558–564.

    Google Scholar 

  9. Siemons, J. and Wagner, A., ‘On the relationship between the length of orbits on k and k+1 subsets’, Abh. Math. Sem. Univ. Hamburg 58 (1988), 267–274.

    Google Scholar 

  10. Stanley, R., ‘Some aspects of groups acting on finite posets’, J. Combin. Theory A, No. 2, 32 (1982), 132–161.

    Google Scholar 

  11. Wagner, A., ‘Orbits on finite incidence structures’, Sympos. Math. Istit. Naz. Alta Mat. 28 (1984), 219–229.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, University of East Anglia, NR4 7TJ, Norwich, U.K.

    Johannes Siemons

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  1. Johannes Siemons
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Siemons, J. On a class of partially ordered sets and their linear invariants. Geom Dedicata 41, 219–228 (1992). https://doi.org/10.1007/BF00182422

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  • DOI: https://doi.org/10.1007/BF00182422

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