On a generalisation of the Dipper-James-Murphy conjecture
نویسنده
چکیده
Let r, n be positive integers. Let e be 0 or an integer bigger than 1. Let v1, · · · , vr ∈ Z/eZ and Kr(n) the set of Kleshchev r-partitions of n with respect to (e;Q), where Q := (v1, · · · , vr). The Dipper–James–Murphy conjecture asserts that Kr(n) is the same as the set of (Q, e)-restricted bipartitions of n if r = 2. In this paper we consider an extension of this conjecture to the case where r > 2. We prove that any multi-core λ = (λ(1), · · · , λ(r)) in Kr(n) is a (Q, e)-restricted r-partition. As a consequence, we show that in the case e = 0, Kr(n) coincides with the set of (Q, e)-restricted r-partitions of n and also coincides with the set of ladder r-partitions of n.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 118 شماره
صفحات -
تاریخ انتشار 2011