3,991 research outputs found
Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity
In 2007, the first author gave an alternative proof of the refined
alternating sign matrix theorem by introducing a linear equation system that
determines the refined ASM numbers uniquely. Computer experiments suggest that
the numbers appearing in a conjecture concerning the number of vertically
symmetric alternating sign matrices with respect to the position of the first 1
in the second row of the matrix establish the solution of a linear equation
system similar to the one for the ordinary refined ASM numbers. In this paper
we show how our attempt to prove this fact naturally leads to a more general
conjectural multivariate Laurent polynomial identity. Remarkably, in contrast
to the ordinary refined ASM numbers, we need to extend the combinatorial
interpretation of the numbers to parameters which are not contained in the
combinatorial admissible domain. Some partial results towards proving the
conjectured multivariate Laurent polynomial identity and additional motivation
why to study it are presented as well
Combinatorial Reciprocity for Monotone Triangles
The number of Monotone Triangles with bottom row k1 < k2 < ... < kn is given
by a polynomial alpha(n; k1,...,kn) in n variables. The evaluation of this
polynomial at weakly decreasing sequences k1 >= k2 >= ... >= kn turns out to be
interpretable as signed enumeration of new combinatorial objects called
Decreasing Monotone Triangles. There exist surprising connections between the
two classes of objects -- in particular it is shown that alpha(n; 1,2,...,n) =
alpha(2n; n,n,n-1,n-1,...,1,1). In perfect analogy to the correspondence
between Monotone Triangles and Alternating Sign Matrices, the set of Decreasing
Monotone Triangles with bottom row (n,n,n-1,n-1,...,1,1) is in one-to-one
correspondence with a certain set of ASM-like matrices, which also play an
important role in proving the claimed identity algebraically. Finding a
bijective proof remains an open problem.Comment: 24 page
What's the Difference Between Professional Human and Machine Translation? A Blind Multi-language Study on Domain-specific MT
Machine translation (MT) has been shown to produce a number of errors that
require human post-editing, but the extent to which professional human
translation (HT) contains such errors has not yet been compared to MT. We
compile pre-translated documents in which MT and HT are interleaved, and ask
professional translators to flag errors and post-edit these documents in a
blind evaluation. We find that the post-editing effort for MT segments is only
higher in two out of three language pairs, and that the number of segments with
wrong terminology, omissions, and typographical problems is similar in HT.Comment: EAMT 2020 (Research Track
Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains
Much recent experimental effort has focused on the realization of exotic
quantum states and dynamics predicted to occur in periodically driven systems.
But how robust are the sought-after features, such as Floquet topological
surface states, against unavoidable imperfections in the periodic driving? In
this work, we address this question in a broader context and study the dynamics
of quantum systems subject to noise with periodically recurring statistics. We
show that the stroboscopic time evolution of such systems is described by a
noise-averaged Floquet superoperator. The eigenvectors and -values of this
superoperator generalize the familiar concepts of Floquet states and
quasienergies and allow us to describe decoherence due to noise efficiently.
Applying the general formalism to the example of a noisy Floquet topological
chain, we re-derive and corroborate our recent findings on the noise-induced
decay of topologically protected end states. These results follow directly from
an expansion of the end state in eigenvectors of the Floquet superoperator.Comment: 13 pages, 5 figures. This is the final, published versio
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