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The structure of the point-line collinearity graph of the maximal2-local geometry for the Monster simple group is investigated.The main results describe the first two discs around an arbitraryvertex. 2000 Mathematics Subject Classification 20D08. 相似文献
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Gerald Höhn 《Advances in Mathematics》2008,217(5):2301-2335
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices. 相似文献
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Professor A. Yu. Garnaev 《International Journal of Game Theory》1992,20(3):269-276
We consider two zero-sum search games in which a searcher moves along a continuous trajectory in a search setQ. The probability of detection depends on the distance between the two players. The problem is open loop, i.e. neither player receives any information about the other as the game progresses. The payoff to a hider is the elapsed time before detection. Optimal mixed strategies are obtained. 相似文献
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We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as α-induction and complete rationality to study extensions of local conformal nets. 相似文献
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John Conway John McKay Abdellah Sebbar 《Proceedings of the American Mathematical Society》2004,132(8):2233-2240
We characterize the 171 discrete subgroups of occurring in Monstrous Moonshine in terms of their group-theoretic properties alone.
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