282,813 research outputs found
Self-complementary plane partitions by Proctor's minuscule method
A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes
the set of arbitrary plane partitions in a box and the set of symmetric plane
partitions as bases of linear representations of Lie groups. We extend this
method by realizing transposition and complementation of plane partitions as
natural linear transformations of the representations, thereby enumerating
symmetric plane partitions, self-complementary plane partitions, and
transpose-complement plane partitions in a new way
Mullineux involution and twisted affine Lie algebras
We use Naito-Sagaki's work [S. Naito & D. Sagaki, J. Algebra 245 (2001)
395--412, J. Algebra 251 (2002) 461--474] on Lakshmibai-Seshadri paths fixed by
diagram automorphisms to study the partitions fixed by Mullineux involution. We
characterize the set of Mullineux-fixed partitions in terms of crystal graphs
of basic representations of twisted affine Lie algebras of type
and of type . We set up bijections between
the set of symmetric partitions and the set of partitions into distinct parts.
We propose a notion of double restricted strict partitions. Bijections between
the set of restricted strict partitions (resp., the set of double restricted
strict partitions) and the set of Mullineux-fixed partitions in the odd case
(resp., in the even case) are obtained
Instantons on ALE spaces and orbifold partitions
We consider N=4 theories on ALE spaces of type. As is well known,
their partition functions coincide with affine characters. We show
that these partition functions are equal to the generating functions of some
peculiar classes of partitions which we introduce under the name 'orbifold
partitions'. These orbifold partitions turn out to be related to the
generalized Frobenius partitions introduced by G. E. Andrews some years ago. We
relate the orbifold partitions to the blended partitions and interpret
explicitly in terms of a free fermion system.Comment: 28 pages, 10 figures; reference adde
Core partitions with distinct parts
Simultaneous core partitions have attracted much attention since Anderson's
work on the number of -core partitions. In this paper we focus on
simultaneous core partitions with distinct parts. The generating function of
-core partitions with distinct parts is obtained. We also prove the results
on the number, the largest size and the average size of -core
partitions. This gives a complete answer to a conjecture of Amdeberhan, which
is partly and independently proved by Straub, Nath and Sellers, and Zaleski
recently.Comment: 8 page
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