Báo cáo toán học: "Combinatorics of Singly-Repairable Families" pptx

... exist singly-repairable subfamilies of Z n 2 of size Θ(2 n /n) for all even n. (ii) There exist singly-repairable subfamilies of Z n 2 of size 2 n+1 n+2 when n is of the form 2 m − 2. Proof. (i) ... from any element of A i to an element of A i±1 and from any element of G i to an element of G i±1 , there is a break/repair path from any element of the B i ∪B i+1 to some...

Ngày tải lên: 07/08/2014, 13:21

... 2. 3 Proofs of the first two Propositions Proof of Proposition 1. This proof relies on this simple standard algorithm for con- verting a list of all partitions of { 1, ,n} into a list of all partitions ... partitions of { 1, ,n+1}: 1. To each partition of { 1, ,n}, add the 1-member-set { n +1} as a new block. This gives a list of some of the partitions of { 1, ,n+1}. 2. To...

Ngày tải lên: 07/08/2014, 13:21

... distinguished elements of B and A. We now check that ϕ is a morphism of algebras by induction on the bidegrees of t and s. We will show that ϕ transforms the products t  λ s of B and t ∗ λ s of  B into ... are elements of a given algebra A. The notion of grafting naturally extends to this context (using the product of A when a merging of angles occurs in (5)), and the cons...

Ngày tải lên: 07/08/2014, 13:21

... ∈ F x }. The degree of x is the size of F x . The tra ce of a set F on another set X is F ∩ X and is denoted by F | X . The trace of a family F of sets is just the family of traces, i.e. F| X = ... same sets of F. The number of sets in F containing both x 1 and x 2 is at most  n−2 k−2  , thus removing these sets from F there remains a family F 1 of subsets of [n] \ {x 1...

Ngày tải lên: 07/08/2014, 21:21

... is then a global sign of (−1) σ where the sign of the pairing σ is the sign of sign of the permutation of the even elements when the parts are arranged in increasing order of their odd parts. In ... π, Pr(π) is a determinant of a submatrix of L. We generalize these results in several ways. Firstly, we give an interpretation (§ 8) of every minor of L in terms of grove p...

Ngày tải lên: 08/08/2014, 01:20

... the set of permutation tableaux of size N + 1, a(T ) is the number of 1s in the first row, b(T ) is the number of unrestricted rows, r(T ) is the number of rows, and w(T ) is the number of superfluous ... the topmost 1 of its column, otherwise it is superfluous. The size of such a permutatio n tableaux is the number of rows of λ plus its number of columns. the electronic jo...

Ngày tải lên: 08/08/2014, 12:23

... V (G). A composition of G is a partition of V (G) into vertex sets of connected induced subgraphs of G. Thus a composition provides a set of connected induced subgraphs of G, {G 1 , G 2 , · · ... composition of a graph G is a partition of the vertex set of G into vertex sets of connected induced subgraphs of G. Knopfmacher and Mays [2] found an explicit formula for C(K m...

Ngày tải lên: 07/08/2014, 13:21

... interrelations of mathematics, geometry and art. The conference resulted in a friendship and an exchange of letters. One of these letters of Coxeter to Escher contained a rendering of a hyperbolic ... rotated version. From the position of a peak, the location of the possible center(s) of rotatio n or axis of translation can be derived. Also the glide distance of a glide re...

Ngày tải lên: 08/08/2014, 01:20

... vertices; in a sense, such tilings are “nearly edge-to-edge”. 4 Proof of Theorem 1 The proof of Theorem 1 breaks up naturally into a sequence of propositions, dealing separately with each possible V 1 . ... then without loss of generality V 2 =(0, 0,c  ). Conversely, every triangle with (0, 4, 2), (0, 0,c  ) ∈V tiles the sphere. Proof: The proof of the first part is similar to that...

Ngày tải lên: 07/08/2014, 13:21

... ANR-05- BLAN-0029-01. Appendix A. Proof of symmetry under interchange of spectral parameters The purpose of this appendix is to provide an explicit proof of the symmetry of the partition function of weighted plane ... center of the lozenge in such a way that the line of v forms an angle of +π/3 with that of u (contrary to the case of three little arches, we cannot get ri...

Ngày tải lên: 07/08/2014, 13:21