Báo cáo toán học: "Enumerative problems inspired by Mayer’s theory of cluster integrals" ppsx

... theoretically from the partition function Z gr by Mayer [22] around 1930. It is the starting point of Mayer’s theory of cluster integrals”. Mayer’s idea consists of setting 1+f ij =exp(−βϕ(| −→ x i − −→ x j |)), ... proving (30) and (34) analytically. the electronic journal of combinatorics 11 (2004), #R32 13 Enumerative problems inspired by Mayer’s theory of clu...

Ngày tải lên: 07/08/2014, 08:20

... tiling of the sphere, see [9] for the foundations of this subject. The study of dihedral f-tilings of the sphere started in 2004 [1, 2, 3], where the clas- sification of all dihedral f-tilings by ... journal of combinatorics 16 (2009), #R87 28 Folding tilings are intrinsically related to the theory of isometric foldings on Rie- mannian manifolds. In fact, the set of singula...

Ngày tải lên: 08/08/2014, 01:20

... path of L 2 (n) the number of VH’s plus the number of VV’s is n, while the number of HV’s plus the number of VV depends on the path. On the other hand, on any path of A 2 (n) the number of HV ... path Q  be obtained from Q by relabeling each noninitial double ascent of Q by one of four pairs, pp, pa, ap,oraa, where each pair of letters designates the presence of res...

Ngày tải lên: 07/08/2014, 06:20

... graphs of degree ≤ 15 and diameter ≤ 10 have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that all of them can in fact be described as lifts of smaller ... computation of spectra of covering graphs [7, 14], the theory of distance-regular graphs [14], a construction of infinitely many cubic 5-arc-transitive graphs [4],...

Ngày tải lên: 07/08/2014, 06:22

... give a constructive proof of an equivalent restatement of Propo- sition 2.5, by looking at the circular classes of permutations τ ∈ S n which fix n. Note that the statement of Proposition 4.4 ( ... this paper was originally motivated by the algebraic discovery of the formula (A). We now give a bijective proof of (A), which is the special case k = n,  = n−1 of Theorem 3.1, na...

Ngày tải lên: 07/08/2014, 06:23

... new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length ... tree D = κ n (p) it is equal, by Theorem 1.1, to the number of inversions). Thus, by now we are able to describe conjecturally the sets of parking functions and trees of gradin...

Ngày tải lên: 07/08/2014, 07:21

... multiple of the product of a finite set of distinct linear factors (ax+ c) and (bx− d) with pairwise coprime natural coefficients, where a | (k − 1) and b | k, b > 1. By now I know only one family of ... holds for unrooted maps of the same types; thus in view of (17) we obtain one more instance of the pattern (2). By duality, any bi-eulerian map admits proper bicolorings bot...

Ngày tải lên: 07/08/2014, 08:22

... the theory of cd-indices of Eulerian posets. 7 Connection to the Tchebyshev posets The self-similarity property of Corollary 6.2 also holds for the duals of the Tchebyshev posets introduced by ... of the possible usefulness of spherical shellings in the theory of orthogonal polynomials. 6 Explicit cd-index formula The proof of Theorem 5.1 motivates to introduce the follo...

Ngày tải lên: 07/08/2014, 08:22

... of simple vertex-labeled set systems with n vertices.) For example, ∗ ITI is supported by the project 1M0021620808 of the Ministry of Education of the Czech Republic. the electronic journal of ... edges. Proof of the Theorem. We prove that, for n →∞, h  n =  1 log 2 + o(1)  n b n =(1.44269 + o(1)) n b n . Let i n be the number of interval partitions Q of [n], weighted as...

Ngày tải lên: 07/08/2014, 08:22

... Consider a copy of H in G. It contains at least one of the components of order m, thus it has at least two vertices of the same color. Therefore there is no rainbow induced subgraph of G isomorphic ... isomorphic. Consider S, a neighborhood of a vertex v of maximum degree in G. Then, all subsets of S of size k − 2 induce isomorphic graphs. Therefore, if |S|≥k we have, by P...

Ngày tải lên: 07/08/2014, 13:21