Báo cáo toán học: "√ On Some Partitions Related to Q( 2)" ppsx

... x + 2y ≡ 7 (mod 8). To see this, we only need to inspect when (−1) n+j is +1 and when it is −1. We leave the details to the reader. 3. Conclusions The partition functions contained in this paper ... intimately related to the arithmetic of Z[ √ 2]. Unfortunately we have little information on the combinatorial behavior o f these functions. We also mention that we may easily manipula...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:20

... α  α + β  β =1. the electronic journal of combinatorics 11 (2004), #R87 3 On Some Non-Holonomic Sequences Stefan Gerhold ∗ Research Institute for Symbolic Computation Johannes Kepler University ... { √ n} n is not holonomic. In addition, we show that {n n } n ,theLambert W function and {log n} n are not holonomic, where in the case of {log n} n we have to rely on an open conjecture...

Ngày tải lên: 07/08/2014, 08:22

... k 2 − 3 2 k+ 1 2 >k 2 −2k +2, a contradiction. These observations lead us to the conclusion that a non-bipartite graph G on 2k − 1 vertices and (2k−2) 2 4 + 1 edges must contain a cycle C k . Consider the last case ... electronic journal of combinatorics 13 (2006), #R55 3 obtain a contradiction with T  (2k − 2,C k )=k 2 − 3k +3, soG − v must be bipartite. It is clear that vertex v mus...

Ngày tải lên: 07/08/2014, 13:21

... X All other partitions contained in A are subdiagrams of some α i . Definition 3.2. For a skew diagram A define the union partition Υ(A) as the union of all partitions α which are contained in ... which is the intersection of all partitions α whose corresponding character [α] appears in [A]. Since we have that skew characters [A] whose skew diagram decays into two partitions A = µ ⊗ ν...

Ngày tải lên: 07/08/2014, 15:22

... u+O(u) ) (3) with some absolute constants in O(·). In the recent decade, a lot of investigations were devoted to the limit distributions of values of additive functions with respect to ν n . Given ... quantity on the right-hand side is also equal to the factor of −C in (23). Inserting these estimates into (2 3) we obtain the desired result (12) for |x|  k 1/6 and k  3. If x  k 1/...

Ngày tải lên: 08/08/2014, 12:22

... Sufficient conditions for circuits in graphs, Proc. London Math. Soc. 24 (1972) 739-755. [5] Radziszowski S.P.: Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey 1, revision #12, ... which belong to each graphs among H 1 , H 2 and H 3 . Let us consider all 30 edges to be of color 1 in (C 4 , C 4 , K 4 − e; 15)-coloring. Finally, consider again the edges of the second...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 09:46

... tree T by Construction 1 is isomorphic to the even part of the Coxeter group of T . No similar group-theoretic interpretation of Construction 2 is known. To conclude this section, I consider briefly ... complete the enumeration in all cases, using Proposition 3.1. 5 Proposition 1.2. A two-graph arises from a tree by Construction 2 if and only if it doesn’t contain the pentagon as an induce...

Ngày tải lên: 07/08/2014, 06:20