a direct proof of the cut principle

... Moreover, there is also a variant of the BCP for self-maps of a non-Archimedean metric space proved by Prieß-Crampe [10] (also see Petalas and Vidalis [9]) It turns out that, in general, the contraction ... obtain only some particular cases of the contraction principle via a discrete argument Finally, we discuss a variant of ET given by Rus [11] (cf Remarks 2.1 and 4.3) Proof of Eilenberg’s theorem ... Actually, a minor modification of the above proof shows that the assumptions of Theorem 1.1 could be weakened: the relations Rn need not be transitive if we assume the uniqueness of a point x...

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 05/08/2014, 09:46

... nonempty cancel out of the above sum, because they are counted once for each subset of S, with alternating signs Thus what survives is the set of placements of d non-taking rooks on the extended board ... for all x Acknowledgments This work was supported in part by a National Science Foundation Graduate Fellowship and a National Science Foundation Postdoctoral Fellowship References [1] T Chow, The ...    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; − x −...

Ngày tải lên: 07/08/2014, 06:20

... counting semistandard tableaux of shape µ/ν satisfying certain properties, and it is a not-toodifficult exercise to show that these two formulations count the same tableaux Via the specialization ν = ... representations of the qanalogue of classical Lie algebras, J Algebra 165 (1994), 295–345 [L] P Littelmann, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent Math 116 (1994), ... Math., to appear [vL] M A A van Leeuwen, The Littlewood-Richardson rule, and related combinatorics, in “Interactions of Combinatorics and Representation Theory,” MSJ Memoirs 11, Math Soc Japan,...

Ngày tải lên: 07/08/2014, 06:23

... of φ−1 when there is a primed integer in the image, we consider only the value of the integer and ignore the prime We leave the details of verifying that φ and φ−1 are inverse maps to the reader ... combinatorial properties of the classical formula, one might hope for a simpler formula For this reason it may be of interest to investigate other q-analogues of the sum of cubes formula In addition, as ... 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...

Ngày tải lên: 07/08/2014, 08:20

... side of a hive (read left-toright) Then a is convex, i.e ≥ (ai−1 + ai+1) Put another way, the list (a1 − a0 , a2 − a1 , , an − an−1) is a weakly decreasing list of integers Proof There are two ... of h’s entries at the two obtuse angles of p is greater than or equal to the sum of h’s entries at the two acute angles of p Proof Add up all the rhombus inequalities from the rhombi inside and ... satisfies the det−1 and Pieri rules Lemma Let p be a lattice parallelogram in the hive triangle trin, with edges parallel to the edges in the triangular lattice, and h a hive of size n Then the...

Ngày tải lên: 07/08/2014, 08:20

... adjacency matrix of the graph is less than ε as long as k ≥ (cε + o(1)) log |G| Their proof involves a clever combinatorial argument that controls the behavior of random walks taken on the ... space V For A ∈ A( V ), we let A denote the operator norm of A equal to the largest absolute value obtained by an eigenvalue of A The cone of positive operators P(V ) = {A ∈ A( V ) | ∀v, Av, v ≥ 0} ... element of the multiset of absolute values of eigenvalues of A( G) As mentioned above, a strong relationship between λ2 (·) and expansion has been achieved In particular, if G is a d-regular graph...

Ngày tải lên: 07/08/2014, 08:20

... and decrease the entry of p that was one larger than p1 by one Let the obtained permutation be p Similarly, decrease q1 by 1, and increase the entry of q that was one larger than q1 by Let the ... = 1, then remove these entries, to get the permutations p∗ and q∗ (After natural relabeling, these are both permutations of length n − 1.) Because of the extreme values of at least one of the ... we know of in which a sequence whose 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...

Ngày tải lên: 07/08/2014, 08:22

... functions, to evaluate the determinant of a Hankel matrix of large Schr¨der numbers Here we use a combinatorial approach that simplifies the o evaluation of the Hankel determinants of large and small Schr¨der ... proof by considering a matrix of order n(n + 1) the determinant of which gives an Their proof is reduced to the computation of the determinant of a Hankel matrix of order n that involves large ... tilings of the Aztec diamond of order n and the set of n-tuples (π1 , , πn ) of large Schr¨der paths satisfying o conditions (A1 ) and (A2 ) Proof: Given a tiling T of ADn , we associate T with an...

Ngày tải lên: 07/08/2014, 08:22

... lower than Cenibra in all parameters Votorantim, Suzano Bahia Sul, Ripasa and International paper are integrated producers of the writing and printing paper By calculating the average of the three ... Klabin and Aracruz that present data for years 2003, 2004 and 2005 and Cenibra which data are available only for 2005 ** The companies not have this value calculated All plants, excepting Aracruz and ... Brazilian companies and comparing with the international Paper performance, the Brazilian group reaches an average lower than foreign subsidiary in five of the six parameters The values reached...

Ngày tải lên: 22/02/2014, 09:20

... special cases of this 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 ... slightly at odds with that of [A7 ] and [A1 0].) The trace formula applies to the case of a global field, and to a finite set of valuations V of F that contains Vram (G, ζ) We recall that Vram (G, ... global theorems, which together amount to a stabilization of each of the terms in the trace formula In the second paper [II], we established a key reduction in the proof of one of the global theorems...

Ngày tải lên: 05/03/2014, 23:20

... White, also, is a name of a thing, or rather of things Whiteness, again, is the name of a quality or attribute of those things Man is a name of many things; humanity is a name of an attribute of ... would cut the matter short by saying, two ideas They would say, that the subject and predicate are both of them names of ideas; the idea of gold, for instance, and the idea of yellow; and that what ... The Calculation Of Chances  Chapter XIX Of The Extension Of Derivative Laws To Adjacent Cases  Chapter XX Of Analogy  Chapter XXI Of The Evidence Of The Law Of Universal Causation  Chapter...

Ngày tải lên: 06/03/2014, 13:20

... is an anchor of {v1 , v2 } if its distances to v1 and v2 are at most 2t0 The two vertices of a quarter that are not on the diagonal are anchors of the diagonal, and the diagonal may have other ... of Λ (a finite cluster of balls in the packing) that is easier to analyze than the full packing Λ The truncation parameter is the first of many decimal constants that appear Each decimal constant ... Proof Suppose that S and S are adjacent quasi-regular tetrahedra with a common face F By the Lemma 2.22, each of the six external faces of this √ pair of quasi-regular tetrahedra has circumradius...

Ngày tải lên: 22/03/2014, 20:20

... satisfaction data at and 18 months using principal component analysis with varimax rotation and Kaiser normalization to ascertain whether the eight factors (Care, Staffing, Development, Relationships, ... intentions and working as a nurse Pay was the only factor, apart from staffing on one occasion, to have a direct effect on intentions There was partial evidence of a direct effect of job satisfaction ... order factor analyse the instrument scores since we could not assume that these factors were the manifestation of a single underlying latent variable Factor analysis of the 6-month data identified...

Ngày tải lên: 18/06/2014, 17:20

... proof of Lemma 2, an argument based on linear programming was used It is slightly more powerful than the cloning here In the proof of Lemma 3, a more sophisticated argument due to Kalai4 , based ... that there is a point in hM of the M convex sets obtained as in Lemma 2, it is sufficient that either one of the original convex sets has at least hM clones, or a proportion of at least i of the ... 3, the available bounds yield a bound on the order of 350 on the number of points needed to meet each polytope (We leave this computation as an exercise for the reader.) On the other hand, the...

Ngày tải lên: 07/08/2014, 06:22

... The “two-path conjecture” states that if a graph G is the edge-disjoint union of two paths of length n with at least one common vertex, then the graph has a third subgraph that is also a path ... to create a new path of length n Therefore, we may assume that s ≥ and that none of {x0 , xn , y0 , yn } is among the s shared vertices We apply a result of Thomason ([8], Theorem 2.1, pages 263-4): ... union of X and Y Theorem If G decomposes into two paths X and Y , each of length n with n ≥ 2, and X and Y have least one common vertex, then G has a path of length n distinct from X and Y Proof...

Ngày tải lên: 07/08/2014, 06:23

... property an exponentially balanced Gray code (cf [10]), as a generalization of (totally) balanced Gray codes Thus, for an exponentially balanced Gray code G(n) one has that the transition count of ... exponentially balanced Gray code, and if n is a power of two, there exists an n-bit totally balanced Gray code Here, we shall present a proof using Theorem 2.1 The proof is constructive like the proof ... A note on balanced Gray codes”, submitted for publication [10] A. J van Zanten and I N Suparta, “Totally balanced and exponentially balanced Gray codes”, Discrete Analysis and Operation Research,...

Ngày tải lên: 07/08/2014, 08:22

... 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 of Lemma Before proceeding with the proof of Theorem 1, ... in P Proof of Theorem For each j in {1, , m}, we may assume that card (Sj ) = nj + (by discarding the extra elements if necessary,) then, using Lemma 2, we find a familly S of scalars (λt j ... ends the proof of Theorem References [1] Alon, N., Combinatorial Nullstellensatz Recent trends in combinatorics (M´traa h´za, 1995) Combin Probab Comput (1999), 7–29 a [2] Shirazi, H and Verstra¨te,...

Ngày tải lên: 07/08/2014, 21:21

... log(d(v)!)1/d(v) = v A 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 ... that H(X) = H ((XA )A A ) by repeated application of Theorem 3, part d) Thus, by the chain rule, H(X) = H ((XA )A A ) = H(XA |XB , B ≺ A) A We are now ready to present the entropy proof of Theorem ... 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...

Ngày tải lên: 08/08/2014, 12:23

... with additional restrictions and an auxiliary parameter However, it was not apparent from those proofs why the above result was so simple and compact We will use the block decomposition method of ... exchanging values c and a at positions j and ℓ) that we must have k = b, so that b is a fixed point of π (This is the additional nice property we obtain by considering pattern 321 instead of 123.) ... of Mansour and Vainshtein [2] to make this much more apparent Proof Let π ∈ Sn contain exactly one occurrence of pattern 321 Let (c, b, a) , c > b > a, be the unique occurrence of 321 in π at positions...

Ngày tải lên: 08/08/2014, 14:23