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A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS

Year 2007, Volume: 2 Issue: 2, 90 - 99, 01.12.2007

Michael Braun

Abstract

Partially ordered sets (X, ≼) and the corresponding incidence algebra I(X, F) are important algebraic structures also playing a crucial role for the enumeration, construction and the classification of many discrete structures. In this paper we consider partially ordered sets X on which some group G acts via the mapping X ×G → X, (x, g) 7→ xg and investigate such incidence functions ϕ : X × X → F of the incidence algebra I(X, F) which are invariant under the group action, i. e. which satisfy the condition ϕ(x, y) = ϕ(xg, yg) for all x, y ∈ X and g ∈ G. Within these considerations we define for such incidence functions ϕ the matrices ϕ∧ respectively ϕ∨ by summation of entries of ϕ and we investigate the structure of these matrices and generalize the results known from group actions on posets.

Keywords

Incidence algebra group action Plesken matrices

References

  • W. Burnside, The Theory of Groups of Finite Order, Cambridge 1911, reprinted by Dover Publications, 1955.
  • S. El-Basil, A. Kerber and E. K. Lloyd, Special issue of MATCH on Tables of Marks in Chemistry, MATCH 46, 2002.
  • A. Kerber, Applied Finite Group Actions, Springer-Verlag, 1998.
  • R. Laue, Eine konstruktive Version des Lemmas von Burnside, Bayreuther Mathematische Schriften 28 (1989), 111-125.
  • R. Laue, Construction of Combinatorial Objects – a Tutorial, Bayreuther Mathematische Schriften 43 (1993), 53-96.
  • W. Plesken, Counting with Groups and Rings, J. Reine Angewandte Mathe- matik 334 (1982), 40-68. Michael Braun Kreuzerweg 23
  • D-81825 Munich Germany
  • E-mail: mic_bra@web.de

Year 2007, Volume: 2 Issue: 2, 90 - 99, 01.12.2007

Michael Braun

Abstract

References

  • W. Burnside, The Theory of Groups of Finite Order, Cambridge 1911, reprinted by Dover Publications, 1955.
  • S. El-Basil, A. Kerber and E. K. Lloyd, Special issue of MATCH on Tables of Marks in Chemistry, MATCH 46, 2002.
  • A. Kerber, Applied Finite Group Actions, Springer-Verlag, 1998.
  • R. Laue, Eine konstruktive Version des Lemmas von Burnside, Bayreuther Mathematische Schriften 28 (1989), 111-125.
  • R. Laue, Construction of Combinatorial Objects – a Tutorial, Bayreuther Mathematische Schriften 43 (1993), 53-96.
  • W. Plesken, Counting with Groups and Rings, J. Reine Angewandte Mathe- matik 334 (1982), 40-68. Michael Braun Kreuzerweg 23
  • D-81825 Munich Germany
  • E-mail: mic_bra@web.de
There are 8 citations in total.

Details

Other ID JA66BV64NV
Journal Section Articles
Authors

Michael Braun This is me

Publication Date December 1, 2007
Published in Issue Year 2007 Volume: 2 Issue: 2

Cite

APA Braun, M. (2007). A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS. International Electronic Journal of Algebra, 2(2), 90-99.
AMA Braun M. A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS. IEJA. December 2007;2(2):90-99.
Chicago Braun, Michael. “A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS”. International Electronic Journal of Algebra 2, no. 2 (December 2007): 90-99.
EndNote Braun M (December 1, 2007) A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS. International Electronic Journal of Algebra 2 2 90–99.
IEEE M. Braun, “A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS”, IEJA, vol. 2, no. 2, pp. 90–99, 2007.
ISNAD Braun, Michael. “A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS”. International Electronic Journal of Algebra 2/2 (December 2007), 90-99.
JAMA Braun M. A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS. IEJA. 2007;2:90–99.
MLA Braun, Michael. “A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS”. International Electronic Journal of Algebra, vol. 2, no. 2, 2007, pp. 90-99.
Vancouver Braun M. A NOTE ON GROUP INVARIANT INCIDENCE FUNCTIONS. IEJA. 2007;2(2):90-9.