Báo cáo toán học: "A short proof, based on mixed volumes, of Liggett’s theorem on the convolution of ultra-logconcave sequences" docx

... (but powerful) representation of the convolution in terms of the product of the corresponding poly- nomials. The original Liggett’s proof does not rely on this representation. 2. Let a = (a 0 , , ... satisfying the Newton inequalities (2) of order m. I.e. we dropped the condition of nonnegativity from the definition of ultra-logconcavity. It is not true that c =...

Ngày tải lên: 07/08/2014, 21:21

... the same second coordinate (i.e., the number of ways of “placing k non-taking rooks on B”). It has long been known [5] that the rook numbers of a board B determine the rook numbers of the complementary ... ···(x−n+1). Then we have the following reciprocity theorem. Theorem. For any board B ⊂ [d] × [d], R(B; x)=(−1) d R(B; − x − 1). The existing proofs derive this as...

Ngày tải lên: 07/08/2014, 06:20

... [X] 4 exists. In the light of Theorems 2 and 3, a positive resolution of the following question would be the best improvement of Theorem 1 possible. Question 1. If X is an order with uncountable character, then ... {1}. Assume to the contrary that there is B ∈ [X] ω with g“[B] 3 = {1}. By the remarks at the beginning of the proof, we may assume without loss of gene...

Ngày tải lên: 07/08/2014, 06:20

... edge e of G, G has a 1-factor containing e, then G has a k-factor containing e and another k-factor avoiding e for all integers k with 1 ≤ k ≤ r − 1. The following example will show that Theorem ... 1)-factor of G avoiding e, then G − E(F 2k+1 ) is a (2m − (2k + 1))- factor containing e, and the proof is complete. Corollary 2 (Kano and Yu [1] 2005) Let G be a connected r-regular gra...

Ngày tải lên: 07/08/2014, 13:21

... give a short proof for the result of Noonan [3] that the number of permutations of length n containing exactly one occurence of pattern 321 is 3 n  2n n−3  . (To be precise, Noonan considered ... Published: Sep 2, 2011 Mathematics Subject Classification: 05A05, 05A15 Abstract We give a short proof for J. Noonan’s result on the number of permutations containing pattern 3...

Ngày tải lên: 08/08/2014, 14:23

... energy consumption, which shows that energy consumption is distributed among the nodes in the rendezvous region. On the other hand, the nodes close to the center of the network consume the highest ... in the calculations. HexDD: In case of HexDD, upon the detection of a new event, the sensor node sends the sensor reading towards one of the border lines and th...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 09:46

... these for the information they contain about trees in addition to partitions and Ferrers diagrams. References [1] G.E.Andrews ,The Theory of Partitions, Encyclopedia of Mathematics 2, Addison- Wesley ... because the restriction D(N) = N k means that N must be a height 2 tree with at least two nests at height one. The crown of N isthedepth-firstnestatheightoneinN. The crown of...

Ngày tải lên: 07/08/2014, 06:22

... extension of the Littlewood-Richardson rule [Z]. Taking the specialization λ = , we obtain the decomposition of s µ/ν into Schur functions; it is simpler than the traditional formulation of the ... another formulation of the Littlewood- Richardson rule— in this case involving the decomposition of s λ s µ into Schur functions. the electronic journal of combinatorics...

Ngày tải lên: 07/08/2014, 06:23

... that the set S consists of pairs of partitions with no primed parts. In the definition of φ −1 when there is a primed integer in the image, we consider only the value of the integer and ignore the ... number of boxes in the first row is equal to the size of the first part, the number of boxes in the second row is equal to the size of the second part, etc...

Ngày tải lên: 07/08/2014, 08:20