Zobrazeno 1 - 10
of 116
pro vyhledávání: '"SHARESHIAN, JOHN"'
We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or ${\mathcal N}$-constrained) groups.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2408.15622
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
Publikováno v:
J. Algebra 659 (2024) 686-697
We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology.
Comment: 14 p
Comment: 14 p
Externí odkaz:
http://arxiv.org/abs/2312.16319
This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the general linear group. We establish the specific conditions under which the
Externí odkaz:
http://arxiv.org/abs/2309.05770
Autor:
Shareshian, John, Sundaram, Sheila
For a fixed nonnegative integer $u$ and positive integer $n$, we investigate the symmetric function \[\sum_{d|n} \left(c_d(\tfrac{n}{d})\right)^u p_d^{\tfrac{n}{d}},\] where $p_n$ denotes the $n$th power sum symmetric function, and $c_d(r)$ is a Rama
Externí odkaz:
http://arxiv.org/abs/2305.12007
We study geometric and topological properties of Hessenberg varieties of codimension one in the type A flag variety. Our main results: (1) give a formula for the Poincar\'e polynomial, (2) characterize when these varieties are irreducible, and (3) sh
Externí odkaz:
http://arxiv.org/abs/2208.06299
Publikováno v:
In Journal of Algebra 1 December 2024 659:686-697
Publikováno v:
Math. Comp. 192 (2023), no. 341, 1349-1361
We verify that every alternating group of degree at most one quadrillion is invariably generated by an element of prime order together with an element of prime power order.
Comment: 14 pages. Code available on github, see https://github.com/Russ
Comment: 14 pages. Code available on github, see https://github.com/Russ
Externí odkaz:
http://arxiv.org/abs/2201.12371
After proving that every Schubert variety in the full flag variety of a complex reductive group $G$ is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide
Externí odkaz:
http://arxiv.org/abs/2107.07929
Autor:
Shareshian, John, Sundaram, Sheila
Publikováno v:
In Journal of Pure and Applied Algebra June 2024 228(6)