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- W78898123 abstract "A generalized Frobenius partition of n, or simply an F-partition, is a two-rowed array of nonnegative integers (a1b1a2b2⋯⋯arbr) in which each row is of the same length and each is arranged in nonincreasing order and n=r+∑ri=1(ai+bi). Such objects were extensively studied by G. E. Andrews [Mem. Amer. Math. Soc. 49 (1984), no. 304; MR0743546 (85m:11063)]. For such F-partitions Andrews defined two enumerating functions φk(n) and cφk(n), where the former function enumerates the F-partitions of n in which the parts repeat at most k times and the latter enumerates those F-partitions of n in which the parts are distinct and are coloured with k given colours. In a recent paper [On Andrews's generalized Frobenius partitions'', Fibonacci Quart., to appear] the author has introduced the function cφk,h(n), which is a generalization of both φk(n) and cφk(n). In the present paper he defines a generalization of the Gaussian polynomials and obtains an expression for CΦk,h(q), the generating function of cφk,h(n) in terms of the Gaussian polynomials. In the last section he examines some conjectures of Andrews that are analogous to the Dyson conjectures." @default.
- W78898123 created "2016-06-24" @default.
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- W78898123 date "1987-01-01" @default.
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- W78898123 title "Some results concerning generalised Frobenius partitions" @default.
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