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.
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
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
Details
| Other ID | JA66BV64NV |
|---|---|
| Authors | |
| Publication Date | December 1, 2007 |
| IZ | https://izlik.org/JA85EF94XH |
| Published in Issue | Year 2007 Volume: 2 Issue: 2 |