proof of the brand bubble
Đề tài " A stable trace formula III. Proof of the main theorems" pptx
... formula In the second paper [II], we established a key reduction in the proof of one of the global theorems In this paper, we shall complete the proof of the theorems We shall combine the global ... argument, the reader can consult the proof of Lemma 5.2 of [A2] and the discussion at the end of Section 10 of [AC].) The terms in the expansion therefore vanish The remaining distribution has ... endoscopic groups Various reductions of the proof have been carried out in other papers, by methods that are generally independent of the trace formula The rest of the proof will have to be established...
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Đề tài " Proof of the Lov´asz conjecture " docx
... 2004 In the summer 2005 an alternative proof of Theorem 2.6 appeared in the preprint [19], and a proof of Conjecture 2.5 was announced by C Schultz Proof of Theorem 1.3 (Lov´sz conjecture) .The case ... and all n 2.3 Completion of the sketch of the proof of the Lov´sz conjecture Cona sider one of the two maps ι : K2 → C2r+1 mapping the edge to the Z2 -invariant edge of C2r+1 Clearly, ι is Z2 ... differentials leads to the proof of the Lov´sz conjecture for the case of even k as well a The results of this paper were announced in [1], where no complete proofs were given The reader is referred...
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Đề tài " A proof of the Kepler conjecture " pdf
... structure of the proof Statement of theorems Basic concepts in the proof Logical skeleton of the proof Proofs of the central claims Construction of the Q-system 2.1 Description of the Q-system ... proof of the main theorem of the chapter A PROOF OF THE KEPLER CONJECTURE 1089 Proof of Theorem 2.9 The rules defining the Q-system specify a uniquely determined set of simplices The proof that they ... paper Here, we describe the top-level outline of the proof and give references to the sources of the details of the proof An expository account of the proof is contained in [Hal00] A general reference...
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The Brand Bubble potx
... powerful brands The grave danger is that brands are losing their way The Brand Bubble explains the greatest risk to world business and how to avoid it If you are in the brand business, only the intuitive ... most of the other theories in the dust Building off the fifteen-year investment Young & Rubicam has made into the proprietary Brand Asset Valuator, John and Ed have captured the concept of energized ... of their enterprises Instead, the majority of brands were stalled in the consumer marketplace, like cars on a Friday afternoon on the 405 cintro.indd 8/25/08 10:34:22 AM The Brand Bubble At the...
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Báo cáo toán học: "A Short Proof of the Rook Reciprocity" pps
... is, and the purpose of this note is to provide such a proof The knowledgeable reader will recognize that the main idea is borrowed from [4] Proof Observe that d (−1) R(B; ... take each other in the final configuration By inclusion-exclusion, we see that the resulting configurations in which the set S of rooks on B is nonempty cancel out of the above sum, because they are ... x extra rows to [d] × [d] Then rk (x + d − k)d−k is the number of ways of first placing k rooks on B and then placing d − k more rooks anywhere (i.e., on B, B or on the extra rows) such that no...
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Báo cáo toán học: " A Purely Combinatorial Proof of the Hadwiger Debrunner (p, q) Conjectur" docx
... every one of our original polytopes will have to contain a proportion g of our points This concludes our proof of the second lemma Proof of Lemma If one of our polytopes has hM clones, then the fact ... of H But there are only |Q|/2 points of Q on each side If we let the points of Q on the two sides of H be QL and QR , we only need meet the convex hulls of proportions 9g/5 of each of these to ... set by the convex hull of the points thus chosen that are within it Obviously a set of points that meets every one of the resulting polytopes will meet each of the original sets Proof of Lemma...
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Báo cáo toán học: " Proof of the Alon-Tarsi Conjecture for n = 2r p" docx
... if there exists g ∈ G such that Lg = M The orbit LG of L under G is the electronic journal of combinatorics (1998) #R28 the G-isotopy class of L The G-autotopism group in G Clearly AG(L) of L ... for any L of order p and any g ∈ G Let R be any set of representatives of the orbits of G in FDLS(p), and let S be a set of representatives of those orbits of size not divisible by p Then fdels(p) ... the truth of the extended conjecture is still unknown for n = 9, the first even value of n which is not of the form given in Corollary is 50, whereas the previous first unknown case of the original...
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Báo cáo toán học: "A Proof of the Two-path Conjecture" pps
... path of length n For example, the complete graph K4 is an edge-disjoint union of two paths of length 3, each path meeting the other in four vertices The cycle C6 is the edge-disjoint union of two ... decompose H By the theorem of Thomason, there is another Hamiltonian decomposition C1 , C2 of H with e in C1 and f in C2 Now we reverse our steps Restore the vertices of degree and remove the edges ... is not a vertex of X, then we replace the edge xn−1 xn with the edge yk+1x0 to create a third path of length n If yk+1 = xi for some i, then we replace the edge xi xi−1 with the edge yk+1x0 to...
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Báo cáo toán học: "A Concise Proof of the Littlewood-Richardson Rule" pdf
... The Details Let P denote the set of nonnegative integer sequences of the form λ = (λ1 ≥ λ2 ≥ · · ·) with finitely many nonzero terms; i.e., the set of partitions We let Pn denote the set of ... and bi free k + 1’s in row i of T , then there should be bi free k’s and free k + 1’s in row i of σk (T ) In the following, T≥j denotes the subtableau of T formed by the entries in columns j, j ... extension of the Littlewood-Richardson rule [Z] Taking the specialization λ = , we obtain the decomposition of sµ/ν into Schur functions; it is simpler than the traditional formulation of the Littlewood-Richardson...
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Báo cáo toán học: "A Combinatorial Proof of the Sum of q-Cubes" pptx
... about a proof described to him by N.M Ferrers The Ferrers shape of a partition is an array of boxes, left justified, in which the number of boxes in the first row is equal to the size of the first ... 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 ... develop q-analogues of those theorems To the best of our knowledge, there exist no combinatorial proofs of q-analogues for powers greater than three the electronic journal of combinatorics 11...
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Báo cáo toán học: "A positive proof of the Littlewood-Richardson rule using the octahedron recurrence" pot
... three of them Let HIVEν denote the set of hives dec dec λµ of size n such that • the lower left entry is zero • the differences on the Northwest side of the hive give λ • the differences on the Northeast ... vertex The vertices of the honeycomb then correspond to the linear regions in the hive The rhombus inequalities on the hive, reinterpreted, state that the edges of the honeycomb are of nonnegative ... the rest of the strip Proposition In the hive ring, bλbωi = bλ+π π∈{0,1} n , π=i λ+π ∈ Zn dec In other words, the hive ring obeys the Pieri rule” Proof Let h be a hive with differences λ on the...
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Báo cáo toán học: "Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem" potx
... below, the elements of graph theory, representation theory, and probability theory required for the statement of the theorem and the subsequent proof The exposition here is primarily for the purposes ... proof of the Alon-Roichman theorem We shall demonstrate tail bounds on the distribution of λ2 (X(G, S)) and conclude from these a strengthened version (Corollary 3) of the following theorem of ... complement of T By the reasoning above, the average of the the electronic journal of combinatorics 11 (2004), #R62 operators R(g) on the space N is zero and the proof may proceed by applying the tail...
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Báo cáo toán học: "A Combinatorial Proof of the Log-concavity of a famous sequence counting permutations" potx
... length is quadratic in terms of the length of the input objects is shown to be log-concave The proof of our claim 2.1 The outline of the proof It is easy to see that the sequence (ak )0≤k≤m is ... , and therefore, it implies the existence of the maps fn,k,l for k < l − 2 That will complete the induction step of our proof 2.2 The details of the proof It is time that we carried out the strategy ... In,k to be the set of all n-permutations with exactly k inversions When there is no danger of confusion about what n is, we will just write Ik instead of In,k The structure of our proof will be...
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Báo cáo toán học: "A Simple Proof of the Aztec Diamond Theorem" potx
... define a path τi from the center of the left-hand edge of the ith row to the center of the right-hand edge of the ith row Namely, each step of the path is from the center of a domino edge (where ... 12 (2005), #R18 Theorem 2.3 (Aztec diamond theorem) The number of domino tilings of the Aztec diamond of order n is 2n(n+1)/2 Remark: The proof of Proposition 2.1 relies on the recurrence relation ... reduced to the computation of the determinant of a Hankel matrix of order n that involves large Schr¨der numbers In this o note we give a proof by means of Hankel determinants of the large and...
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Báo cáo toán học: "Proof of the Razumov–Stroganov conjecture for some infinite families of link patterns" pdf
... ANR-05BLAN-0029-01 Appendix A Proof of symmetry under interchange of spectral parameters The purpose of this appendix is to provide an explicit proof of the symmetry of the partition function of weighted plane ... originating from one of the sides of length c and ending at the other, see Fig (ii), which simply follow two types of tiles out of the three One can replace the local Boltzmann weights of the tiles with ... facts: Theorem of [9] The components of Ψn are homogeneous polynomials of total degree n(n − 1), and of partial degree at most n − in each variable zi Theorem of [9] The entries Ψn,π of the groundstate...
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Báo cáo toán học: "An elementary proof of the hook formula" ppt
... (5) The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the fundamental theorem of algebra, and the proof of (5) is a simple geometric argument Proof of (3) The ... bijective proofs However, these have the disadvantage of appearing somewhat complicated to those readers unfamiliar with probability theory or the combinatorics of Young diagrams Other proofs have the ... interested in the connections which the proof reveals In the section 4, we apply the proof to the shifted tableaux case Acknowledgements The author is grateful to Adriano Garsia for pointing out the q,...
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Báo cáo toán học: "A duality based proof of the Combinatorial Nullstellensatz Omran Kouba" pps
... and achieves the proof of Lemma Before proceeding with the proof of Theorem 1, let us recall that the total degree of a polynomial P from K[X1 , , Xm ] is the largest value of d1 + d2 + · · · ... combination of the elements of the basis (µt )t∈S This proves the existence of a familly of scalars (λS )t∈S , such that t S ϕm (P ) = t∈S λt µt (P ) for any polynomial P in Km [T ], and achieves the proof ... ,d2 , ,dm )∈D Finally, the conclusion of the theorem follows since m λS11 λS22 · · · λSm P (t1 , t2 , , tm ) = Φ(P ) = t t t (t1 , ,tm )∈S1 ×···×Sm This ends the proof of Theorem References [1]...
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Báo cáo toán học: "Proof of the combinatorial nullstellensatz over integral domains, in the spirit of Kouba" docx
... substantially), and it is the purpose of the present note to try to lay bare the basic mechanism of Kouba’s proof Proof of Theorem The proof of the Theorem will be based on the following simple lemma ... generalizations thereof throughout the paper The present author wishes to emphasize that the proof in the present paper differs from Kouba’s proof only in the setting and the way in which the coefficients ... direct proof of the full Theorem Two relevant recent articles ought to be mentioned A very short direct proof of Theorem was given by Michalek in [5] who explicitly remarks that the proof works...
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Báo cáo toán học: "An entropy proof of the Kahn-Lov´sz theorem a" ppsx
... proof of the Kahn-Lov´sz theorem a The entropy proof of the Kahn-Lov´sz theorem is complicated by the fact that there can a be edges of the graph (and a fixed matching) amongst the neighbors of ... The original proof of Kahn and Lov´sz was never published, see [3] Friedland’s proof a is based on an extension of Schrijver’s [10] proof of the Br`gman inequality A short proof, e deducing the ... understanding our proof of the Kahn-Lov´sz, which we present in Section a Radhakrishnan’s proof This section presents the entropy proof of Radhakrishnan of Br`gman’s theorem, which e is as follows Theorem...
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