3,279 research outputs found
Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions
The -Young lattice is a partial order on partitions with no part
larger than . This weak subposet of the Young lattice originated from the
study of the -Schur functions(atoms) , symmetric functions
that form a natural basis of the space spanned by homogeneous functions indexed
by -bounded partitions. The chains in the -Young lattice are induced by a
Pieri-type rule experimentally satisfied by the -Schur functions. Here,
using a natural bijection between -bounded partitions and -cores, we
establish an algorithm for identifying chains in the -Young lattice with
certain tableaux on cores. This algorithm reveals that the -Young
lattice is isomorphic to the weak order on the quotient of the affine symmetric
group by a maximal parabolic subgroup. From this, the
conjectured -Pieri rule implies that the -Kostka matrix connecting the
homogeneous basis \{h_\la\}_{\la\in\CY^k} to \{s_\la^{(k)}\}_{\la\in\CY^k}
may now be obtained by counting appropriate classes of tableaux on -cores.
This suggests that the conjecturally positive -Schur expansion coefficients
for Macdonald polynomials (reducing to -Kostka polynomials for large )
could be described by a -statistic on these tableaux, or equivalently on
reduced words for affine permutations.Comment: 30 pages, 1 figur
Explicit formulas for the generalized Hermite polynomials in superspace
We provide explicit formulas for the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in
superspace. The construction relies on the triangular action of the Hamiltonian
on the supermonomial basis. This translates into determinantal expressions for
the Hamiltonian's eigenfunctions.Comment: 19 pages. This is a recasting of the second part of the first version
of hep-th/0305038 which has been splitted in two articles. In this revised
version, the introduction has been rewritten and a new appendix has been
added. To appear in JP
Influence of a local change of depth on the behavior of bouncing oil drops
The work of Couder \textit{et al} (see also Bush \textit{et al}) inspired
consideration of the impact of a submerged obstacle, providing a local change
of depth, on the behavior of oil drops in the bouncing regime. In the linked
videos, we recreate some of their results for a drop bouncing on a uniform
depth bath of the same liquid undergoing vertical oscillations just below the
conditions for Faraday instability, and show a range of new behaviors
associated with change of depth.
This article accompanies a fluid dynamics video entered into the Gallery of
Fluid Motion of the 66th Annual Meeting of the APS Division of Fluid Dynamics.Comment: High and low resolutions videos included as ancillary file
Missing the Forest for the Trees: The Seventh Circuitâs Refinement of Bloom \u27s Private Gain Test for Honest Services Fraud in \u3cem\u3eUnited States v. Thompson\u3c/em\u3e
Public officials, as well as public employees, owe the public the fiduciary duty of providing their honest services. The mail fraud statute, 18 U.S.C. § 1341, proscribes using the mails to carry out âany scheme or artifice to defraud.â It further defines, in § 1346, âany scheme or artifice to defraudâ to include âa scheme or artifice to deprive another of the intangible right of honest services.â In passing these statutes, Congress never defined the terms âscheme or artifice,â âintangible rightâ or âhonest services.â Because of this failure, the appellate courts have adopted limiting principles to prevent minor breaches of fiduciary duties from becoming federal crimes. The Seventh Circuit adopted the limiting principle âmisuse of office for private gainâ in United States v. Bloom. Recently, the court refined the Bloom standard in United States v. Thompson holding that âneither an increase in salary for doing what one\u27s superiors deem a good job, nor an addition to one\u27s peace of mind, is a âprivate benefit.ââ This holding conflicts with previous case law from the District Court for the Northern District of Illinois, concluding that oneâs job or the prospect of future employment can be a private gain under Bloom. Because the Seventh Circuit appears to have distinguished Thompson from the cases in the Northern District of Illinois rather than overruling them, the court may have inadvertently created a loophole through which public employees can engage in âsubtle schemesâ and not be punished under § 1346. This Note concludes that the Seventh Circuit could have distinguished Thompson from the Northern District cases on the grounds that a âscheme,â as defined in its normal usage, existed is those cases, but did not exist in Thompson. The Note further argues that had the court made a threshold determination of whether or not a âschemeâ existed in Thompson, it would not have had to reach the private gain issue, thereby preventing the problems raised after Thompson
Alien Registration- Lapointe, Charles J. (Jackman, Somerset County)
https://digitalmaine.com/alien_docs/7039/thumbnail.jp
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