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- W2048784051 abstract "LetS(q, d) be the maximal numberv such that, for every general position linear maph: Δ(q−1)(d+1) →R d, there exist at leastv different collections {Δ t1, ..., Δ t q} of disjoint faces of Δ(q−1)(d+1) with the property thatf(Δ t1) ∩ ... ∩f(Δ t q) ≠ Ø. Sierksma's conjecture is thatS(q, d)=((q−1)!) d . The following lower bound (Theorem 1) is proved assuming thatq is a prime number: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaacI% cacaWGXbGaaiilaiaadsgacaGGPaGaeyyzIm7aaSaaaeaacaaIXaaa% baGaaiikaiaadghacqGHsislcaaIXaGaaiykaiaacgcaaaWaaeWaae% aadaWcaaqaaiaadghaaeaacaaIYaaaaaGaayjkaiaawMcaamaaCaaa% leqabaWaaSGbaeaacaGGOaGaaiikaiaadghacqGHsislcaaIXaGaai% ykaiaacIcacaWGKbGaey4kaSIaaGymaiaacMcacaGGPaaabaGaaGOm% aaaaaaGccaGGUaaaaa!4F90! $$S(q,d) geqslant frac{1}{{(q - 1)!}}left( {frac{q}{2}} right)^{{{((q - 1)(d + 1))} mathord{left/ {vphantom {{((q - 1)(d + 1))} 2}} right. kern-nulldelimiterspace} 2}} .$$ Using the same technique we obtain (Theorem 2) a lower bound for the number of different splittings of a “generic” necklace." @default.
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- W2048784051 date "1993-04-01" @default.
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- W2048784051 title "Note on a conjecture of sierksma" @default.
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- W2048784051 doi "https://doi.org/10.1007/bf02189327" @default.
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