Results 41 to 50 of about 220,490 (165)
Mixed Eulerian numbers and Peterson Schubert calculus [PDF]
, 2023 Let $\Phi$ be a root system. Postnikov introduced and studied the mixed $\Phi$-Eulerian numbers. These numbers indicate the mixed volumes of $\Phi$-hypersimplices.
Horiguchi, Tatsuya
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Schubert calculus in Lie groups [PDF]
, 2023 Let $G$ be a Lie group with a maximal torus $T$. Combining Schubert calculus in the flag manifold $G/T$ with the Serre spectral sequence of the fibration $G\rightarrow G/T$, we construct the integral cohomology ring $H^{\ast}(G)$ uniformly for all ...
Duan, Haibao
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Advances in Mathematics, 1997 20 pages (LaTeX). To appear in Advances in Mathematics. The quantum Pieri formula in the original version has been corrected (see also alg-geom/9705024), and the Title has been ``quantized''
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Dynamic Pole Assignment and Schubert Calculus [PDF]
SIAM Journal on Control and Optimization, 1996 The output feedback pole assignment problem is a classical problem in linear systems theory. In this paper we calculate the number of complex dynamic compensators of order $q$ assigning a given set of poles for a $q$-nondegenerate $m$-input, $p$-output system of McMillan degree $n = q(m + p - 1) + mp$. As a corollary it follows that when this number is
Ravi, M S +2 more
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International Journal of Mathematics and Mathematical Sciences, 2006 We discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures
Cenap Özel, Erol Yilmaz
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Quasisymmetric Schubert calculus
, 2022 32 ...
Pechenik, Oliver, Satriano, Matthew
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Characteristic numbers and chromatic polynomial of a tensor
Forum of Mathematics, SigmaWe introduce the characteristic numbers and the chromatic polynomial of a linear subspace of matrices, or equivalently of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of ...
Austin Conner, Mateusz Michalek
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Frontiers of reality in Schubert calculus [PDF]
Bulletin of the American Mathematical Society, 2009 The theorem of Mukhin, Tarasov, and Varchenko (formerly the Shapiro conjecture for Grassmannians) asserts that all (a priori complex) solutions to certain geometric problems in the Schubert calculus are actually real. Their proof is quite remarkable, using ideas from integrable systems, Fuchsian differential equations, and representation theory.
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Free fermionic probability theory and k-theoretic schubert calculus
Forum of Mathematics, SigmaFor each of the four particle processes given by Dieker and Warren, we show the n-step transition kernels are given by the (dual) (weak) refined symmetric Grothendieck functions up to a simple overall factor. We do so by encoding the particle dynamics as
Shinsuke Iwao +2 more
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