Báo cáo toán học: "Counting Simplexes in R 3" ppt

... interested in this paper in the number of simplexes contained in some H⊆ n , which we denote by simp(H). This investigation is particularly interesting for H spanning n and containing no collinear vectors. Our ... contains no collinear vectors, simp(H) is minimal if and only if H is contained in two planes intersecting in H, one of contains exactly three vectors of H; i.e. precise...

Ngày tải lên: 07/08/2014, 06:22

... communication. [13] H. J. Ryser, Neuere Problem in der Kombinatorik, in Vortraheuber Kombinatorik, Oberwohlfach (1967), 69-91. [14] S. K. Stein, Transversals of Latin Squares and their generalizations, Pacific ... indebted to Ran Ziv for a stimulating remark, and to Noga Zewi for proving Corollary 2.8. References [1] R. Aharoni, E. Berger and R. Ziv, Indep endent systems of representativ...

Ngày tải lên: 08/08/2014, 01:20

... starting at t in which the number corresponding t o m (namely, t) is not minimal. By similar reasoning, there are  k m+1  S n−ℓ+1 non-primary occurrences of τ in which the number corresponding to ... 231 in α (corresponding to 352, 251 , and 472) and two occurrences of τ = 212 (corresponding to 535 and 525). Note that here we are requiring that the letters within some word correspondi...

Ngày tải lên: 08/08/2014, 11:20

... rafacosta@deb.uminho.pt; Miguel Rocha - mrocha@di.uminho.pt; Eug´enio C. Ferreira - ecferreira@deb.uminho.pt; Bruce Tidor - tidor@mit.edu; Isabel Rocha - irocha@deb.uminho.pt; ∗ Corresponding author Abstract Systems ... early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. Biosystems 83(2-3):136–151 Breitling R, Gilbert D, Heiner M, Orton R...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:20

... Every planar graph has a crossing-free drawing. A long standing open problem involving edge-lengths, due to Harborth et al. [21, 22, 26], asks whether every planar graph has a crossing-free drawing ... in contrast to our result that graphs of bounded degree have arbitrarily large distance-number. A graph is d-realizable if, for every mapping of its vertices to (not-necessarily distinct) poi...

Ngày tải lên: 07/08/2014, 21:20

... entries of τ generate D m . We transform τ into the canonical form (r 0 , r 0 , r 1 , r 1 ). Proof. τ ∼ (r 0 , r 1 , r k , r k−1 ) ∼ (r 0 , r 1 , r 2 , r 1 ) ∼ (r 0 , r 0 , r 1 , r 1 ) The main ... The results of our paper are complementary to the work in [5], since our results are derived from first principles using what is perhaps a more intuitive approach. the...

Ngày tải lên: 08/08/2014, 12:23

... flag-transitive (v 3 ) and (v 4 ) configurations of small order containing information on the number and symmetry types of corresponding rotary polygons. 1 Introduction Various problems regarding ... onfiguration permits no antimorphisms, every rotary polygon is necessarily weakly-rotary, and every reflexive rotary polygon in necessarily genuinely reflexive. Moreover, every such configuration is...

Ngày tải lên: 08/08/2014, 14:23

... ν  k n− 2r = 1 r  r γ  n− 2r  ρ=0  1+n − 2r − ρ n − 2r − ρ  ρ + r − 1 ρ  n − r r − γ − 1  k n− 2r = 1 r  r γ  n − r +1 n − 2r  n − r r − γ − 1  k n− 2r . In the following result we consider the remaining three ... s  k n− 2r (24) where 0 ≤ γ ≤ r. After expanding F ˆq (x, y, t) into a geometric series and using the previous relations we will obtain...

Ngày tải lên: 07/08/2014, 08:22

... 2i − r/ k, r 2 /k, (r r 2 )/k − i   2j j, 2j − r/ k, r 2 /k, (r r 2 )/k − j  , where r = r 1 + 2r 2 . Proof. According to Theorem 3.5, the expression  k |r φ(k) 4r  2r/ k r/ k  2 counts realizations of ... is given by 2 r 2r 2  r r 2 , r 2 , r − 2r 2  = 2 r 2r 2  r 2r 2  2r 2 r 2  . (5) Proof. The generating function for elements in B takin...

Ngày tải lên: 08/08/2014, 14:23