Authors: Vučić, Aleksandar
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Note on a conjecture of sierksma
Journal: Discrete and Computational Geometry
Volume: 9
Issue: 1
First page: 339
Last page: 349
Issue Date: 1-Dec-1993
ISSN: 0179-5376
DOI: 10.1007/BF02189327
Abstract: 
Let S(q, d) be the maximal number v such that, for every general position linear map h: Δ(q-1)(d+1) →Rd, there exist at least v different collections {Δt1, ..., Δtq} of disjoint faces of Δ(q-1)(d+1) with the property that f(Δt1) ∩ ... ∩f(Δtq) ≠ Ø. Sierksma's conjecture is that S(q, d)=((q-1)!)d. The following lower bound (Theorem 1) is proved assuming that q is a prime number: {Mathematical expression} Using the same technique we obtain (Theorem 2) a lower bound for the number of different splittings of a "generic" necklace.
Publisher: Springer Link

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