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) ? x^g and investigate such incidence
functions ? : X × X ? F of the incidence algebra I(X, F) which are invariant
under the group action, i. e. which satisfy the condition ?(x, y) = ?(x^g, y^g) for
all x, y ? X and g ? G. Within these considerations we define for such incidence
functions ? the matrices ?^? respectively ?^? by summation of entries of
? and we investigate the structure of these matrices and generalize the results
known from group actions on posets.
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Author Name: Michael Braun
URL: View PDF
Keywords: Keywords: Incidence algebra; group action; Plesken matrices.
ISSN: 1306- 6048