Báo cáo toán học: "(−1)–enumeration of self–complementary plane partitions" ppsx

... (−1)–enumeration of self–complementary plane partitions in terms of SC(a, b, c), the ordinary enumeration of self–complementary plane partitions. Theorem 2. The enumeration of self–complementary plane partitions ... of self–complementary plane partitions is needed. It will also be used as a step in the proof of the (−1)–enumeration. Theorem 1 (Stanley [14]). The nu...

Ngày tải lên: 07/08/2014, 08:22

... ν},whereS 3 is some subset of m  − 1elementsofS 0 ∪ S 1 and T 3 is some subset of n  − 1elementsofT 0 ∪ T 1 . From the previous section we know that the determinant of this transformation is ... →∞through integer multiples of m/t. Proof. The theorem is an example of an Edgeworth expansion. We need the case of multivariable lattice distributions, such as Corollary 22.3 of [3]....

Ngày tải lên: 07/08/2014, 13:21

... the problem of enumeration of planar near-triangulations, solved by Tutte in [9] using the method of recursive decomposition. The same method, applied to the problem of enumeration of triangulations ... planar map is a class of equivalence of embedded graphs G → S 2 by the homeomor- phisms of S 2 . We note by V (G), E(G) and F (G) the sets of vertices, edges and faces of...

Ngày tải lên: 07/08/2014, 15:23

... of (13) and (17) are equal for infinitely many values of r and t, and we use a polynomial argument to complete the proof. The proof of equation (18) is similar to that of (14) using the idea of ... the sets A x of paths as events, meaning the set of of paths with the property specified in the definition of A x . For future reference, note also that A 0 corresponds to the set of...

Ngày tải lên: 08/08/2014, 12:23

... efficients of F are negligible compared to those of A because of Comment 2 above. We will use these ideas without explicit mention when considering error bounds. 4 Proof of Theorem 1 The value of A g (r) ... for the number of labelled k-connected graphs of orientable genus g for k ≤ 3. 1 Introducti on The exact enumeration of various types of maps on the sphere (or, equivalent...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 05/08/2014, 15:20

... r n into reflections of W n , its sequence of labels (l(r 1 ), ,l(r n )), is a bijection from the set of all factorizations to the set of type B parking functions. For example the label of the factorization (−1 ... the set of all such factorizations to the set of parking functions. The above considerations show that this is just a rephrasing of Stanley’s Theorem 3.1. We shall g...

Ngày tải lên: 07/08/2014, 06:23

... journal of combinatorics 14 (2007), #R30 5 2 Some self-similar matrices. The theory of partially ordered sets (posets in the remaining of this paper) will guide us to produce an analogue of equation ... motivates the use of the name “zeta matrix” in the context of a general poset. the electronic journal of combinatorics 14 (2007), #R30 4 We start by the following interpretation...

Ngày tải lên: 07/08/2014, 15:22

... properties of cyclic permu- tations of r. In Section 3, we consider more general cases. 2 Properties of cyclic permutations of a sequence In this section, we study pro perties of cyclic permutations of ... contradiction. the electronic journal of combinatorics 17 (2010), #R117 9 [4] A. Brandt, A generalization of a combinatoria l theorem of Sparre Andersen about sums of r...

Ngày tải lên: 08/08/2014, 12:22

... nanowires, the reason for the observation of their similar reversible capacities was because of the agglomeration of NiMoO 4 nanowires and the resulting restriction of the electronic conduction paths ... capacity limitations (theoretical capacity of 372 mA h/g), initial loss of capacity, and structural deformation [1, 2], one of the current areas of interest in lithium-io...

Ngày tải lên: 20/06/2014, 21:20