Báo cáo toán học: "Planar maps as labeled mobiles" potx

... clockwise around unlabeled vertices: a vertex labeled n is followed by a vertex or flag labeled at least n − 1, while a flag labeled n is followed by a vertex or flag labeled at least n. Denoting by ... (2.1), (2.2) and (2.3). 4.2. Maps with arbitrary valences The case of arbitrary planar maps with prescribed face valences may be seen as yet another particular case of Eulerian plan...

Ngày tải lên: 07/08/2014, 08:20

... exceeds C n is non-decreasing as we move from labeled to unlabeled graphs. Thus it suffices to prove Theorem 3 for the labeled case. We only need to choose anetworkG + 1 which has a nontrivial automorphism ... t(1) that was claimed in Theorem 2. Lemma 2 Let y 0 = y 0 (t) be as defined in (5). Then y 0 (t) has an analytic inverse function for t ∈ T  ,andy 0 (t) increases from 0 to ∞ as...

Ngày tải lên: 07/08/2014, 07:21

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

... number of labeled (and unlabeled) tour- naments which have the given score vector (see e.g. [7], [6], and references therein). Although the problem of counting the number of labeled (or unlabeled) ... one of the N s cases, d(X t+1 ,Y t+1 )=d(X t ,Y t ) = 1, and in the last case d(X t+1 ,Y t+1 )=d(X t ,Y t ) − 1=0, so that we obtain the inequality stated in the lemma. This is basically bec...

Ngày tải lên: 07/08/2014, 06:20

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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

... implies (2). (2) implies (3) is easy. Now, assume that (3) holds. We will show that M a (S) ∗ has a left invariant mean. To every finite subset F in S and each >0, we associate the nonempty subset Ω F, = ... µ. It is easy to see that A is a left Banach S -module. By assumption, there exists a net (µ α )inP (S) such that T µ α → T in the weak ∗ operator topology of B (A ∗∗ ). We may assume...

Ngày tải lên: 06/08/2014, 04:21

... 1996; Accepted: January 31, 1997 Abstract Two classification schemes for Steiner triple systems on 15 points have been proposed recently: one based on the binary code spanned by the blocks, the ... shown here that the two approaches are equivalent. 1991 AMS Classification: Primary: 05B07; Secondary: 11H06, 94B25. 1 Introduction It has been known since 1919 [1919] that there are 80 Steiner tripl...

Ngày tải lên: 07/08/2014, 06:20