Báo cáo toán học: "Permutations, cycles and the pattern 2–13" pdf

... nonempty and closed sub- sets of B X such that lim n à(A n ) = 0, the set A = n=1 A n is nonempty and convex. (iv) The measure à satises the Cantor property in X. Proof. The equivalence of (i) and ... subsets of the bounded and convex set coC, then à(C n ) = 0 (n ∈ N), and therefore C ∞ = ∅. Appealing again to the ˇ Smulian theorem [6, Theorem V.6.2] we find t...

Ngày tải lên: 20/06/2014, 20:20

... time- domain order-distributions and the Laplace-domain logarithmic operator. This paper has presented a theory of Laplace-domain logarithmic operators. The motivation is the appeara nce of logarithmic ... demonstrates that the ln(s) operator appears frequently. The next section will review the necessary results from fractional calculus and the theory of order-d...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

... 2-matroids Let Q 1 and Q 2 be 2-matroids. When Q 1 and Q 2 have the same ground-set and skew classes we shall use Q 1 + Q 2 to denote the parity system which is the sum of Q 1 and Q 2 . When Q 1 and Q 2 have ... since r 1 (A) ≤ r t 1 (A) ≤ r 1 (A) + 1 and r 1 (A) ≤ r ˜ t 1 (A) ≤ r 1 (A) + 1. Parity Systems and the Delta-Matroid Intersection Problem Andr´e Bouc...

Ngày tải lên: 07/08/2014, 06:20

... proof of Theorem 2. 2.2 Proof of Theorem 3 Here we assume that s 2 ≥  2 n,thecases 1 ≥  2 nis similar. Denote by P r the product of the primes not exceeding r. The rough outline of the proof will ... denote the greatest common divisor and [a, b] the least common multiple of integers a, b. Consider the coprime graph on the integers. This is the graph whose v...

Ngày tải lên: 07/08/2014, 06:22

... terminology of dimension 2 posets, an increasing subsequence is a chain and a decreasing subsequence is an anti-chain. Permutations which are the union of an increasing and a decreasing subsequence M.D. ... figure the vertical and horizontal lines have the obvious separation meaning; for example, if R and W are red and white points we would ha...

Ngày tải lên: 07/08/2014, 06:22

... asymptotic formula for f nk from theorem 1.1, together with standard results from random matrix theory relating the behavior of the eigenvalues of random unitary matrices to the behavior of the eigenvalues of ... restricted increasing subsequence length. Section 1 states and proves the connection between the classical increasing sub- sequence problem and the unitary gr...

Ngày tải lên: 07/08/2014, 06:22

... #R18 4 Monomial nonnegativity and the Bruhat order Brian Drake, Sean Gerrish, Mark Skandera Dept. of Mathematics, Brandeis University MS 050, P.O. Box 9110, Waltham, MA 02454 bdrake@math.brandeis.edu Dept. ... that the coefficient of m 1 s in the monomial expansion of h h à is negative. the electronic journal of combinatorics 11(2) (2005), #R18 3 Note that the ratio of...

Ngày tải lên: 07/08/2014, 08:22

... alternations either with blocks of the form π (k, + ) for  + >or of the form π (k, − ) for  − <, and horizontal alternations with blocks of the form π (k + ,) for k + >kor of the form π (k − ,) for ... than the nth Fibonacci number for some n .The definition of sub-2 n−1 is analogous. the electronic journal of combinatorics 13 (2006), #R54 9 Grid c...

Ngày tải lên: 07/08/2014, 13:21

... Furthermore, the cycle structure is obviously preserved. The seven patterns involved the above theorem share the property that they are equidistributed with the non-cyclic occurrences. Let Π(p) denote the ... unique pair of N and S steps. (The rightmost N step to the left of the F step ending at the F step’s level is paired with the leftmost S step to the right of th...

Ngày tải lên: 07/08/2014, 13:21

... circuits and G is not ordinary. ✷ Theorem 4.3 If neither G[X] nor G[X] is bipartite, then G is not ordinary. Proof: By hypothesis, b(G) + p(G) ≥ 2, and so the result follows from Theorem 2.3. ✷ The ... 1-factors.) In the next section we derive the existence or otherwise of the set S described earlier by relating the dimensions of the spaces L(G), C(G), E(G) and A(G). 2 A...

Ngày tải lên: 07/08/2014, 15:22

... S and S  merge A, or both S and S  merge B, then, by Theorem 2.2, (ii) holds. Furthermore, making use of the note, the argument for the case that one of the sequences, S say, merges A and the ... of the quartets collected by S  , but no other quartet in Q. Assume that ab|cd is a quartet collected by U k . Then either a, b ∈ A k and c, d ∈ X − A k , or c, d ∈ A k an...

Ngày tải lên: 07/08/2014, 21:20