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cellular behavior and scanning electron microscope evaluation of pro-root mta, root mta and modified mta on fibroblast l929
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15 صفحه اولPermutation statistics on involutions
In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...
متن کاملSmoothness of Schubert Varieties via Patterns in Root Subsystems
The aim of this article is to present a smoothness criterion for Schubert varieties in generalized flag manifolds G/B in terms of patterns in root systems. We generalize Lakshmibai-Sandhya’s well-known result that says that a Schubert variety in SL(n)/B is smooth if and only if the corresponding permutation avoids the patterns 3412 and 4231. Our criterion is formulated uniformly in general Lie ...
متن کاملA Classification of Subsystems of a Root System
We classify isomorphic classes of the homomorphisms of a root system Ξ to a root system Σ which do not change Cartan integers. We examine several types of isomorphic classes defined by the Weyl group of Σ, that of Ξ and the automorphisms of Σ or Ξ etc. We also distinguish the subsystem generated by a subset of a fundamental system. We introduce the concept of the dual pair for root systems whic...
متن کاملA Statistic on Involutions
We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I (n)denote the set of all involutions on [n](= {1, 2, . . . , n}) and let F(2n)denote the set of all fixed point free involutions on [2n]. For an involution δ, let |δ| denote the number of 2-cycles in δ. Let [n]q = 1+q+· · ·+qn−1 and let (k)q denote the q-binomial coefficient....
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2010
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089510000054