Báo cáo toán học: "On sums over partially ordered sets" ppsx

... electronic journal of combinatorics 6 (1999), #R34 2 2. Sums over partially ordered sets We assume that the reader is familiar with partially ordered sets, which are subse- quently referred to as ... x 0 is maximal in P , then this sum is empty, and hence the statement trivially holds. We On sums over partially ordered sets Klaus Dohmen Institut f¨ur Informatik Humboldt-Un...

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... ∂M d so that P c 0 is semihyperbolic, then all (finite) periodic points of P c 0 are repelling. Moreover, the set ω(0) of accumulation points of the orbit of 0 is a hyperbolic set of P c 0 . Thus ... P −n c 0 (V ε (x)) for n ≥ 0, the map P n c 0 : V → V ε (x) has degree at most d and diam(V )<B 0 θ n .Moreover the complement of J c 0 is a John domain; this means that J c 0 is locally connec...

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... known that [M] each of the sets {h λ }, {m λ },and{p λ },whereλ ranges over all partitions of n, is a basis of the vector space over of symmetric functions homogeneous of degree n. 15 References [G] ... t exp wzt 1+zt  n first, and then apply Θ w combinatorially to the set. Consider a labelled ordered n-tuple (S 1 ,S 2 , ,S n ) of possibly empty, ordered sets of all possible sizes. Th...

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... the sum on the left is less than the square of the sum on the right, and we may disregard these sums. Since d λ  >e λ  it suffices to show that there exists a k independent of λ such that c λ  − ... (nq−i)/(n−i)fori =1, 2, 3. Let µ be the shape obtained from λ by removing the first row. Then the sums in the previous equations correspond to c µ , d µ and e µ .Set r := |µ| = n − λ 1 = n(1...

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... 65C50 Abstract We consider a game in which players select strings over { 0, 1 } and observe a series of fair coin tosses, interpreted as a string over { 0, 1 }. The winner of this game is the player whose ... in the maximum overlap of a suffix of σ with a prefix of σ  , where the strings σ and σ  have common length n; and the notation L n (σ) for L n (σ, σ), disallowing for the trivial ove...

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... Aronszajn and Panitchpakdi [1], we propose a similar concept in partially ordered sets. Definition 2.1. Let (X, ≺) be a partially ordered set. A subset M of X is called exter- nally complete if ... first to extend it to the case of partially ordered sets. Definition 3.1. Let X be a partially ordered set. The ordered pair (S, T) of two self- maps of the set X is called a Bana...

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... >f −1 (aN)  + ∞  i=N+1 P  |X 1 | >f −1 (ai)   . Almost Sure Convergence of Weighted Sums of I.I.D. Random Variables 41 lim sup n |X n c n | = lim sup n |X n | log 1/β n · c n log 1/β n ... Ann. Math. Statist. 37 (1966) 1482–1493. 2. Y. S. Chow and T. L. Lai, Limiting behavior of weighted sums of independent random variables, Ann. Pr obab. 1 (1973) 810–824. 3. Y. S. Chow and H....

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... canonical covering is close to the minimal possible. 3 Lower bound for the length of covering Let N  ¯α, ¯ β  stand for a disjoint coset, i.e. one of the cosets in the disjoint covering. As it ... forms over linear functions (Theory and Appli- cations), Yerevan Univ., Yerevan, (1990), 201p., (in Russian) [4] A. Aleksanyan and R. Serobyan, Coverings associated with quadratic equations ove...

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