Báo cáo toán học: "An inverse matrix formula in the right-quantum algebra" ppt
Báo cáo toán học: "An inverse matrix formula in the right-quantum algebra" ppt
... prove the right-quantum Jacobiratio theorem, and we use the matrix inverse formula to find a generalization of the (right-quantum) MacMahon master theorem.1 IntroductionCombinatorial linear ... p-sequence in the order they appear, then all the steps starting at height2 in the p-sequence in the order they appear, etc. Clearly, this map preserves the type of the sequence. the electronic ... include ieither have it in α (and possibly in β) or they have it only in β. There is an obvioussign-reversing involution between the former and the latter – just move the cycleof α containing i...
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Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx
... point in t(P ⊕ Q) can be assigned uniquely to a lattice point in tPby projection onto the RdPcoordinate. Further, as P is reflexive, all of the lattice points in RdPare contained in the ... journal of combinatorics 13 (2006), #N15 5interesting that the Ehrhart polynomial and the Ehrhart series are “dual” to each other in this sense. It would also be interesting to find other examples ... (5).Therefore, to count the lattice points in t ((H ∩ P ) ⊕ (K ∩ Q)) we can count the latticepoints in ∩iˆHi∩∩jˆKj∩t (P ⊕ Q). This we can do by using our partition (3) from the proof...
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Báo cáo toán học: "An On-Line Version of the Encyclopedia of Integer Sequences" doc
... of the on-line version, but will be important when[4] becomes available.) The %O, or “offset”, line contains two numbers. The first gives the subscript of the initial term in the sequence (in the ... the sequence in the lexicographic order in the table is determined by the terms of the sequence beginning at this point.Rule 4. The sequence must be well-defined and interesting. Ideally it should ... uses. The on-line version provides a rapid lookupservice for identifying sequences, locating them in the literature, or producing further terms. The Maple package will in addition try to find formulae,...
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Báo cáo toán học: " An Eigenvalue Characterization of Antipodal Distance-Regular Graph" ppt
... (standard) independencenumber of the k-th power of the graph, and the study of the limit case in which sucha bound is attained.Let us now fix the terminology and notation used throughout the paper. ... (that is, the sets of antipodal vertices) have all cardinality r, a numberdepending on the order and the eigenvalues of the graph. This result is obtainedvia an spectral bound for the k-independence ... distinctvertices are in the same class iff they are at distance D (see, for instance, Godsil [17].) If all the fibres have the same cardinality, say r,wesaythatΓisanr-antipodalgraph.We index...
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Báo cáo toán học: "An alternative definition of the notion valuation in the theory of near polygons" pot
... hyperplane in the projective space PG(6, 3). Let E1be the following point-line geometry: (i) the points of E1are the points of PG(6, 3) \ PG(5, 3);(ii) the lines of E1are the lines of PG(6, ... and z distinct fromy. Then f (v) = f(y). The line uv is a line through u ∈ Fxcontaining a point with valuef(u) − 1, namely the point v. By the induction hypothesis, uv ⊆ Fx. Since also ... the lines through x contained in Giare precisely the lines of Li∩ L. Now, by [7,Section 4.6], the convex subspace G1, G2 intersects F1 in G1and F2 in G2. Hence, the set of lines...
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Báo cáo toán học: "Iodine Alters Gene Expression in the MCF7 Breast Cancer Cell Line: Evidence for an Anti-Estrogen Effect of Iodine" doc
... 2-methoxyestradiol, decreasing 3, 4-estradiol quinone or indirectly via the inactivation of E2. The importance of the CYP1A1/CYP1B1 ratio in- vivo is evident in the increased presence of 4-OH-E2 in breast ... iodine/iodide could enhance the efficacy of Tamoxifen therapy: 1) having an additive effect on estrogen inhibition and 2) inhibiting the expression of CCND1 thus preventing or slowing the ... through 1) up-regulating proteins involved in estrogen metabolism (specifically through increas-ing the CYP1A1/1B1 ratio), and 2) decreasing BRCA1 inhibition thus permitting its inhibition of estrogen...
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Báo cáo toán học: "Efficient covering designs of the complete graph" pptx
... since theyhold for L3. We must show that the third invariant holds initially, when j = 0. Indeed, in L3,all the edges adjacent to a vertex of S are either non-covered, or covered once in ... ConcludingremarksandanopenproblemWhenH=Kh,theconstantn0(H)inTheorem1.1isshownintheprooftobenolargerthanmax{h8,h1+h(h−1)},whereh1=h1(h)isthecorrespondingconstantinWilson’sTheorem.However,thebestknownboundforh1(and,consequently,forn0(H)),isratherlarge,andhighlyexponentialinh[7].Itisplausible,however,thatthestatementofTheorem1.1isstillvalidforn0(H)whichismuchsmaller.Infact,weconjecturethefollowing:Conjecture3.1ThereexistsapositiveconstantCsuchthatforallh≥2,ifn≥Ch2thenKnhasaKhcoveringdesignwhereeachedgeiscoveredatmosttwiceandanytwocopiesintersectinatmostoneedge. the ... twice.2. 1-intersection:AnytwocopiesofHintersect in at most one edge.3. Efficiency: s|EH| <n2+ c(H) · n,wheresis the number of members in the covering, andc(H) is some constant depending...
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Báo cáo toán học: "Graphs with chromatic roots in the interval (1, 2)" doc
... continuitythat the chromatic polynomial has a root in the interval (1, 2).We can perform a similar analysis on the graphs obtained by adding the single edgev1v4to X(s, t) with the following ... maybe it is the toughness of hamiltonian graphs(rather than the actual cycle itself) that is important, and along these lines Dong & Kohhave made the following interesting strengthening of Thomassen’s ... (−1)s+t. In particular, when either s or t is odd, thenP(X(s, t), 2) = −2.Proof. The derivative of P (X(s, t), x) can be obtained by differentiating each of the 27terms in the chromatic...
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Báo cáo toán học: "Compression of root systems and the E-sequence" pptx
... isomorphism, the roots decorating the vertices will have changed. Furthermore, the construction of˜Drespects the fact that the edges in the Dynkin diagram represent the inner products of the the electronic ... 42These are the simple roots of E8, which span the E8lattice. They correspond to the vertices v1, . . . , v8of Dyn(E8), in the order shown on the right. This ordering of simple the ... is easy to determine as well. By Theorem 3.3.3 this isdetermined by the links in T(V ). For any x ∈ Γ7, the set of y ∈ Γ7orthogonal to x can the electronic journal of combinatorics 15 (2008),...
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Báo cáo toán học: "A Rainbow k-Matching in the Complete Graph with r Colors" pdf
... and r ≥ 2 then we canfind easily a rainbow 2-matching, but we may not find a ra inbow 3-matching. Generally,if n ≥ 2k + 1 then the following colorings do not allow a rainbow k-matching to exist.(See ... monochromatic. In the coloring(b), a complete subgraph Kn−(k−2)of G is monochromatic and the other edges are rainbow. In each coloring, it is clear that there is no rainbow k-matching. However, if there ... Eroh, Linda: Rainbow Ramsey numbers of stars and matchings, Bull. Inst. Combin.Appl. 40 (2004), 91–99.[4] Eroh, Linda: Constrained Ramsey numbers of matchings, J. Combin. Math. Combin.Comput....
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