Báo cáo toán học: "Certificates of factorisation for chromatic polynomials" pot

... 1: Numbers of chromatic polynomials of degree at most 10. (A) Total number of chromatic polynomials, (B) number of chromatic polynomials of clique-separable g r aphs and (C) number of chromatic ... 4705 Table 2: Chromatic factorisations of chromatic polynomials of degree n ≤ 10 of strongly non-clique-separable graph. 4 Certificates of Factorisation Definition A...

Ngày tải lên: 07/08/2014, 21:21

... family of gra phs have chromatic factorisations that satisfy this certificate. A certificate of factorisation is a sequence of steps that explains the chromatic factori- sation of a given chromatic ... an infinite family of strongly non-clique-separable graphs that have a chromatic factorisation and give a certificate of factorisation for these factorisations. 2 Graphs...

Ngày tải lên: 07/08/2014, 21:21

... Journal of Mathematics 34:3 (2006) 295–305 Global Existence of Solution for Semilinear Dissipative Wave Equation MD. Abu Naim Sheikh 1 and MD. Abdul Matin 2 1 Department of Math., Dhaka Univ. of Engineering ... in (0, ∞) ×(a, b), u(0,x)=u 0 (x),u t (0,x)=u 1 (x) for x ∈ (a, b), u(t, a)=u(t, b) = 0 for any t>0, (1.1) Global Existence of Solution for Semilinear Dissipative...

Ngày tải lên: 06/08/2014, 05:20

... southeast corners of the components of the diagram. The essential set E(w)ofapermutationw is defined to be the set of white corners of the diagram of w. For every white corner (i, j)ofw,itsrank is ... Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two c...

Ngày tải lên: 07/08/2014, 06:20

... Cayley table of G is invariant with the enumeration chosen for G, so to complete the proof of the theorem it suffices to exhibit a 2-partition of L. We do this by first arguing that each of the subsquares ... 1-partition. For A 11 this follows from Theorem 4 since A 11 is a Cayley table for N, which is a group of odd order (the main diagonal is always a transversal of the Cayle...

Ngày tải lên: 07/08/2014, 06:23

... the matrix formed by reversing the order of the rows of M. As for the matrix P of 3.1.3(2), we have seen above that it is the integral encoding of the rectification S of any tableau T of which M ... Note that the potential for e increases as one descends the ladder. The condition of having a too large a potential for e determines a lower portion containing M of the ladder...

Ngày tải lên: 07/08/2014, 13:21

... referee of this journal for pointing out the second exception of the case n = 10 in the proof of Lemma 4. References [1] F. Blanchet-Sadri, E. Clader, and O. Simpson. Border correlations of partial ... word β(w) of the same length where the ith letter tells whether the ith conjugate w  = vu of w = uv is bordered or not. Let [u] denote the set of conjugates of the word w. We...

Ngày tải lên: 07/08/2014, 15:22

... e −Ω(n) . Proof The proof follows that of Lemma 6.6 of [3], which deals with the case when m = n − (β + o(1))(n/ ln n) for fixed β > 0 (see [1] for details). We may now prove our aforementioned result for ... without a set of more than r edge-disjoint copies of C). For L ∈ J c n , let S(L) denote a maximal set of edge-disjoint copies of C (so |S(L)|  r) and, for s  r...

Ngày tải lên: 08/08/2014, 11:20

... interpretation for the Stirling number of the second kind. Corollary 2. The integer S(n, k) is the number of partitions of [n] in k blocks. For a partition π = {B 1 , B 2 , . . . , B k } of [n] in ... combinatorial interpretation for two sequences which are multiples of the central factorial numbers of odd indices a nd we also establish a simple derivation of the explicit...

Ngày tải lên: 08/08/2014, 12:22

... polynomials ex- panded in terms of the monomial basis. The top row of such a matrix is a list of monomial functions, the entries of the sub-diagonal are of the form −(rα + s), with r and s ∈ N + , ... quasi-triangular nature of these matrices gives a recursion for the Jack polynomials allowing for efficient computation. A specialization of these results yields a determinantal...

Ngày tải lên: 07/08/2014, 06:20