Báo cáo toán học: "Multi-statistic enumeration of two-stack sortable permutations" pptx

... express the (−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 ... remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removi...

Ngày tải lên: 07/08/2014, 08:22

... journal of combinatorics 12 (2005), #R29 17 Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums E. Rodney Canfield ∗ Department of Computer Science University of ... 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 tran...

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 ... the asymptotical enumeration of arbitrary rooted maps on surfaces, and by Gao ([3, 4]) to the asymptotical enumeration of triangulations. Similar equations appear under t...

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) ... derive asymptotic formulas 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...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 05/08/2014, 15:21

... from the beginning of this proof. Thus, in either case x is locally equivalent to y, and the theorem is proved. ✷ PROOFOFTHEOREM2. The proof below exactly follows the proof of Proposition 5.1 ... transversals of V are locally equivalent, and the distance between any two of them does not exceed 2n − 1. Some examples of thick subsets: one-element sets, cycles of size 3, subspaces o...

Ngày tải lên: 07/08/2014, 06:20

... parameters of σ. The parameters of the empty permutation (of length 0) are (1, 1). Note that for any permutation, p ≤ q. Lemma 10 ([37]) Let σ be a 1234-avoiding permutation of length n ≥ 0, of parameters (p, ... equation (4). We the electronic journal of combinatorics 9 (2003), #R19 10 2.3 The number of descents and the Tutte polynomial of planar maps A number of refinements...

Ngày tải lên: 07/08/2014, 07:21

... examples of fixing sets of non-trivial finite groups are of the form {1, . . . , k } for some k. If the fixing set of every non-trivial finite group is of this form, then the computation of a fixing ... element of the stabilizer of S. This clearly requires at least ⌈ n−1 k+1 ⌉ vertices, so fix(Inf k (K n )) = ⌈ n−1 k+1 ⌉. It seems likely that the proof of Theorem 1 6 could extend...

Ngày tải lên: 07/08/2014, 21:21

... by  X k  the set of all k-subsets of X. A hypergraph H = (V ; E) is said to be k-uniform if E ⊂  V k  (the cardinality of any edge is equal to k). We shall always assume that the set of vertices V of a ... cardinality of any orbit of τ . Note that τ β = id V n (where id V n is the identity of the set V n ). For every vertex v ∈ e we have clearly τ (v) ∈ e, hence every orbi...

Ngày tải lên: 08/08/2014, 12:22