Báo cáo toán học: "Combinatorics of Partial Derivatives" pdf

... 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

... 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 element of (A 0 |G 0 ). ... number of 1’s is even, one has the same parity for the number of 1’s in the rest of the positions of v. the electronic journal of combinatorics 12 (2005), #R59 10 (b) there...

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

... while we can view the additive group of (F q ) 6 as (GF (q 3 )) 2 , taking the q 3 + 1 hyperplanes. Each of the sets D i will consist of a union of q 3 +1 q+1 of these hyperplanes. Using the constructions ... p 2 rows. Each of the D i except for D 0 and D p will consist of taking only those elements of order p 2 (elements in G  − pG  ) from p −1 of the rows and combining t...

Ngày tải lên: 07/08/2014, 21:20

... 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

... conversely). This gives 2 n+2 strict pin words of size n and concludes the proof. The proof of Theorem 4.1 2 follows the structure of the proof of Theorem 3.4 in [16]. Lemma 4.11. [16, Lemma ... oscillation ξ of size n − 1 by the addition of either a minim al element at the beginning of ξ or a maximal element at the e nd of ξ, followed by a flip of an element of ξ according...

Ngày tải lên: 08/08/2014, 14:22

... We assume without loss of generality that C(e 0 ) is admissible. Moreover, e 0 ∈ HE(C(e 0 )) ⇐⇒ The first dart of e 0 appears in the tour of T before the second one. Proof. The proof of the lemma, by ... denominator of the reduced form of Ψ P is known (Bou07). In this article, the first author has investigated the effects of elementary transformations of the Hasse diagram of a...

Ngày tải lên: 08/08/2014, 01:20

... definition of the quantum yield as follows: # of emitted photons # of absorbed photons Φ ≡ , (3) the number of emitted photons indicates the multiplication of the quantum yield and the number of ... morphologies of HeLa cells cultured on a flat PDMS surface. Quantification of Aβ peptides via detection of FITC We investigated the applicability of our p-FET sensor t...

Ngày tải lên: 20/06/2014, 20:20

... crlin@ntut.edu.tw 1 Department of Mechanical Engineering and Institute of Manufacturing Technology, National Taipei University of Technology, Taipei, 106, Taiwan Full list of author information is available at the end of ... beamline of the National Synchrotron Radiation Research Center (NSRRC). This work was financially supported by the main research projects of the National Sc...

Ngày tải lên: 20/06/2014, 20:20