Báo cáo toán học: "Partitions, rooks, and symmetric functions in noncommuting variables" pdf

... Tevlin, L., Thibon, J Y., Thiem, N., Venkateswaran, V., Vinroot, C. R., Yan, N., and Mike, Z. Supercharacters, symmetric functions in no ncommut ing variables, and related Hopf algebras. Preprint ... Rosas, M., and Zabrocki, M. Invariants and coinvariants of t he symmetric groups in noncommuting variables. Canad. J. Math. 60, 2 (20 08), 266–296. [4] Chen, W. Y. C., Li, T....

Ngày tải lên: 08/08/2014, 14:23

... all chains in T  ,sonodesinchains in C’s subtree are embedded to the right of those in chains in T  .Lets = starter(C )and t = terminator(C). No node with a chain in C’s tree has y coordinate ... disconnect P ,andsothex-edges of P form a bond separating V and V . It follows that Θ x is a simple closed curve containing all faces corresponding to subsets containing x in its int...

Ngày tải lên: 07/08/2014, 08:20

Ngày tải lên: 05/08/2014, 15:21

... other hand, bearing in mind that µ and ν are in the interior of the same Weyl chamber C,andwµ = µ + and wν = ν + are dominant, we may use Proposition 4.4 to compare the ranks of x(µ)andx(ν) in the ... , including the cross section X and the subspace V .Moreover,V also carries a standard ordering relative to the root system Φ; however, these two “standard” orderings of V coincide:...

Ngày tải lên: 07/08/2014, 08:22

... dealing with the empty strip. Let c min = −λ  1 +1 and c max = λ 1 −1. Let φ h (or φ e ) be the horizontal (resp. vertical) border strip starting with the box having content c min and ending ... each inverse operation is still over the ring Λ of symmetric functions. Thus C(Π) and C(Π  ) are stably equivalent over Λ. (c) i ∈ Q Π ,i+1∈ P Π ,P Π  = P Π and Q Π  = Q Π . Suppose th...

Ngày tải lên: 07/08/2014, 08:22

... 4-cycle containing both v 1 and v 2 or containing both v 3 and v 4 . Proof. Suppose, to the contrary, that there is a 4-cycle containing both v 1 and v 2 or containing both v 3 and v 4 . By symmetry, ... H v contains an edge {v 1 ,v 2 ,v 5 } containing v 1 and v 2 ,and an edge {v 3 ,v 4 ,v 5 } containing v 3 and v 4 . Since the edges N(v i ), 1 ≤ i ≤ 4, are deleted from H G when...

Ngày tải lên: 07/08/2014, 13:21

... k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in ... the minimum cardinality taken over all maximal k-irredundant sets of vertices of G. In 1975, Meir and Moon [10] introduced the concept of a k-dominating set (called a ‘k-covering’ in...

Ngày tải lên: 07/08/2014, 15:22

... maximal independent set and that in every graph, γ(G) ≤ i(G) ≤ β(G) where γ(G) and i(G) are respectively the minimum cardinality of a dominating set and of an independent dominating set and β(G) ... Hedetniemi and S. T. Hedetniemi, Alliances in graphs, JCMCC 48 (2004), 157-177. [7] N. Linial, D. Peleg, Y. Rabinovich and M. Saks, Sphere packing and local majorities in graph...

Ngày tải lên: 07/08/2014, 21:20

... Diestel and D. K¨uhn. On in nite cycles II. Combinatorica , 24:91–116, 2004. [15] R. Diestel and D. K¨uhn. Topological paths, cycles and spanning trees in infinite graphs. Europ. J. Combinatorics, ... ny arc in |G| with on e endpoint in X and one in Y contains an edge from F . 4 Euler tours In this section we prove Theorem 1.3, but before we do so let us consider an example...

Ngày tải lên: 07/08/2014, 21:21

... of the embedding factor w ′ = 343 which has embedding index 5, and the two 2’s of u are in po sitions 6 and 7. Note that we obtain ordinary factor order by taking P to be an antichain. Also, we will ... “weakly increasing” and “maximum” have their usual meanings. Also, let w +m be the result of applying the + operator m times. By using the previous lemma a nd induction, we obtain the...

Ngày tải lên: 08/08/2014, 01:20