منابع مشابه
Generalized triangulations, pipe dreams, and simplicial spheres
We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding northeast chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable and thus a shellable sphere. In particular, this implies a positivity result for Schubert polynomials. For ...
متن کاملDuality of Antidiagonals and Pipe Dreams
The cohomology ring H(F ln) of the manifold of complete flags in a complex vector space C has a basis consisting of the Schubert classes [Xw], the cohomology classes of the Schubert varieties Xw indexed by permutations w ∈ Sn. The ring H (F ln) is naturally a quotient of a polynomial ring in n variables; nonetheless, there are natural n-variate polynomials, the Schubert polynomials, representin...
متن کاملOn the Relationship between Pipe Dreams and Permutation Words
Pipe dreams represent permutations pictorially as a series of crossing pipes. Recent applications of pipe dreams include the calculation of Schubert polynomials, fillings of moon polyominoes, and in the combinatorics of antidiagonal simplicial complexes. These applications associate pipe dreams to words of elementary symmetric transpositions via a canonical mapping. However, this canonical mapp...
متن کاملPipe Dreams: Tapping into the Health Information in Our Sewers.
The emerging field of sewage chemical-information mining is taking advantage of a readily available yet underappreciated resource: the untreated waste flowing under our feet and the biosolids remaining after treatment. It turns out that sewage and sewage sludge hold a wealth of data on chemical consumption and exposure, and potentially even the health status of whole communities. EHP A Section ...
متن کاملNeuroimaging: Separating the Promise from the Pipe Dreams
Colorful brain images may tempt researchers to make claims that outpace solid scientific data—and may tempt the public to believe those claims. In particular, although brain imaging has provided solid evidence of alterations in brain structures and functions associated with many psychiatric disorders, it can be used neither to diagnose such disorders nor to determine exactly how treatments work...
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ژورنال
عنوان ژورنال: Nature Materials
سال: 2010
ISSN: 1476-1122,1476-4660
DOI: 10.1038/nmat2729