Vicious walkers and Young tableaux I: without walls
نویسندگان
چکیده
We rederive previously known results for the number of star and watermelon configurations by showing that these follow immediately from standard results in the theory of Young tableaux and integer partitions. In this way we provide a proof of a result, previously only conjectured, for the total number of stars.
منابع مشابه
Vicious Walkers, Friendly Walkers, and Young Tableaux. III. Between Two Walls
1 Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria. 2 Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia; e-mail: [email protected] 3 LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France. 4 Present address: Institut Gerard Desargues, Université Claude Bernard Lyon-I, Bâtiment B...
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We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of n-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absen...
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تاریخ انتشار 1998