论文信息 - On Counting the k-face Cells of Cyclic Arrangements

On Counting the k-face Cells of Cyclic Arrangements

In this paper, we compute the exact number of k -face cells of the cyclic arrangements which are the dual to the well-known cyclic polytopes. The proof uses the combinatorial interpretation of arrangements in terms of oriented matroids.

David Forge | Jorge L. Ramírez Alfonsín | J. R. Alfonsín | David Forge

[1] János Pach,et al. Rich cells in an arrangement of hyperplanes , 1995 .

[2] B. Grünbaum. Arrangements and Spreads , 1972 .

[3] B. Sturmfels. Oriented Matroids , 1993 .

[4] R. W. Shannon. Simplicial cells in arrangements of hyperplanes , 1979 .

[5] I. G. MacDonald,et al. CONVEX POLYTOPES AND THE UPPER BOUND CONJECTURE , 1973 .

[6] C. Carathéodory. Über den variabilitätsbereich der fourier’schen konstanten von positiven harmonischen funktionen , 1911 .

[7] Jean-Pierre Roudneff. Quadrilaterals and pentagons in arrangements of lines , 1987 .

[8] Jean-Pierre Roudneff. Cells with many facets in arrangements of hyperplanes , 1991, Discret. Math..

[9] C. Carathéodory. Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen , 1907 .

[10] Jim Lawrence,et al. Oriented matroids , 1978, J. Comb. Theory B.

[11] P. McMullen. The maximum numbers of faces of a convex polytope , 1970 .

[12] Bernd Sturmfels,et al. Simplicial cells in arrangements and mutations of oriented matroids , 1988 .