In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2012, vol. 53, no. 2, p. 451-460
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In: Advances in Geometry, 2007, vol. 7, no. 2, p. 177-189
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In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2012, vol. 53, no. 2, p. 451-460
The growth function W(t) of a Coxeter group W relative to a Coxeter generating set is always a rational function. We prove by an explicit construction that there are infinitely many cocompact Coxeter groups W in hyperbolic 4-space with the following property. All the roots of the denominator of W(t) are on the unit circle except exactly two pairs of real roots.
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In: European Journal of Combinatorics, 2008, vol. 29, no. 3, p. 601-616
We define so-called poset-polynomials of a graded poset and use it to give an explicit and general description of the combinatorial numbers in Schläfli’s (combinatorial) reduction formula. For simplicial and simple polytopes these combinatorial numbers can be written as functions of the numbers of faces of the polytope and the tangent numbers. We use the constructed formulas to determine the...
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