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- W2345787963 abstract "We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. The game arises from the well-known chip-firing game when the usual relation of equivalence defined on the set of all configurations is replaced by a suitable partial order. The set all firing sequences of length m that the player is allowed to perform in the Yamanouchi toppling game is shown to be in bijection with all standard Young tableaux whose shape is a partition of the integer m with at most n-1 parts. The set of all configurations that a player can obtain from a starting configuration is encoded in a suitable formal power series. When the graph is the simple path and each monomial of the series is replaced by a suitable Schur polynomial, we prove that such a series reduces to Hall-Littlewod symmetric polynomials. The same series provides a combinatorial description of orthogonal polynomials when the monomials are replaced by products of moments suitably modified." @default.
- W2345787963 created "2016-06-24" @default.
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- W2345787963 date "2014-12-01" @default.
- W2345787963 modified "2023-09-27" @default.
- W2345787963 title "Hall-Littlewood symmetric functions via Yamanouchi toppling game" @default.
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