Zobrazeno 1 - 10
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pro vyhledávání: '"HORIGUCHI, TATSUYA"'
Foata and Sch\"{u}tzenberger gave an expansion for the Eulerian polynomial $A_n(t)$ in terms of the basis $\{t^j(1+t)^{n-1-2j}\}$ for the space of polynomials $f(t)$ satisfying $f(t)=t^{n-1}f(1/t)$. We generalize this result in two ways. First, we pr
Externí odkaz:
http://arxiv.org/abs/2405.09242
Autor:
Horiguchi, Tatsuya
Regular nilpotent Hessenberg varieties are subvarieties of full flag varieties, while regular nilpotent partial Hessenberg varieties are subvarieties of partial flag varieties. In this manuscript we first provide a summand formula and a product formu
Externí odkaz:
http://arxiv.org/abs/2405.07247
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot acti
Externí odkaz:
http://arxiv.org/abs/2310.16235
Autor:
Harada, Megumi, Horiguchi, Tatsuya
This manuscript is a contributed chapter in the forthcoming CRC Press volume, titled the Handbook of Combinatorial Algebraic Geometry: Subvarieties of the Flag Variety. The book, as a whole, is aimed at a diverse audience of researchers and graduate
Externí odkaz:
http://arxiv.org/abs/2305.14089
Autor:
Horiguchi, Tatsuya, Shirato, Tomoaki
Dale Peterson has discovered a surprising result that the quantum cohomology ring of the flag variety $\mbox{GL}_n(\mathbb{C})/B$ is isomorphic to the coordinate ring of the intersection of the Peterson variety $\mbox{Pet}_n$ and the opposite Schuber
Externí odkaz:
http://arxiv.org/abs/2302.06041
Autor:
Horiguchi, Tatsuya
Peterson varieties are subvarieties of flag varieties and their (equivariant) cohomology rings are given by Fukukawa-Harada-Masuda in type A and soon later the author with Harada and Masuda gives an explicit presentation of the (equivariant) cohomolo
Externí odkaz:
http://arxiv.org/abs/2208.02440
Given a root system $\Phi$ of type $A_n$, $B_n$, $C_n$, or $D_n$ in Euclidean space $E$, let $W$ be the associated Weyl group. For a point $p \in E$ not orthogonal to any of the roots in $\Phi$, we consider the $W$-permutohedron $P_W$, which is the c
Externí odkaz:
http://arxiv.org/abs/2105.05453
Autor:
Horiguchi, Tatsuya
Let $\Phi$ be a root system. Postnikov introduced and studied the mixed $\Phi$-Eulerian numbers. These numbers indicate the mixed volumes of $\Phi$-hypersimplices. As specializations of these numbers, one can obtain the usual Eulerian numbers, the Ca
Externí odkaz:
http://arxiv.org/abs/2104.14083
We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric viewpoint, and p
Externí odkaz:
http://arxiv.org/abs/2104.02914