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Hyperplanes of the form xj = xi + c are called affinographic. For an affinographic hyperplane arrangement in Rn, such as the Shi arrangement, we study the function f(m) that counts integral points in [1,m]n that do not lie in any hyperplane of the arrangement. We show that f(m) is a piecewise polynomial function of positive integers m, composed of terms(More)
The main content of the note is a proof of the conjecture of Hamidoune-Las Vergnas on the directed switching game in the case of Lawrence oriented matroids. C.E. Shannon has introduced the switching game for graphs circa 1960. It has been generalized and solved for matroids by A. Lehman [4]. A switching game on graphs and oriented matroids was introduced by(More)
In this paper we discuss Alpha Galois lattices (Alpha lattices for short) and the corresponding association rules. An alpha lattice is coarser than the related concept lattice and so contains fewer nodes, so fewer closed patterns, and a smaller basis of association rules. Coarseness depends on a a priori classification, i.e. a cover C of the powerset of the(More)
Let M be a matroid on [n] and E be the graded algebra generated over a field k generated by the elements 1, e1, . . . , en . Let =(M) be the ideal of E generated by the squares e2 1, . . . , e 2 n , elements of the form ei e j + ai j e j ei and ‘boundaries of circuits’, i.e., elements of the form ∑ χ j ei1 . . . ei j−1 ei j+1 . . . eim , with χ j ∈ k and(More)