Results 71 to 80 of about 369 (191)
Orders of Finite Reductive Monoids
, 2008 We show four formulas for calculating the orders of finite reductive monoids with zero. As applications, these formulas are then used to calculate the orders of finite reductive monoids induced from the $F_q$-split $\J$-irreducible monoids $\overline {K^* (G_0)}$ where $G_0$ is a simple algebraic group over the algebraic closure of $F_q$, and $ : G_0\
Li, Zhuo, Li, Zhenheng, Cao, You'an
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The six operations in topology
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract In this paper, we show that the six functor formalism for sheaves on locally compact Hausdorff topological spaces, as developed, for example,‐ in Kashiwara and Schapira's book Sheaves on Manifolds, can be extended to sheaves with values in any closed symmetric monoidal ∞$\infty$‐category which is stable and bicomplete. Notice that, since we do
Marco Volpe
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A Monoid for the Grassmannian Bruhat Order
European Journal of Combinatorics, 1999 If \(S_\infty\) denotes the group of permutations on the natural numbers fixing all but a finite number then \(u\in S_\infty\) may be used to define Schubert polynomials \(S_u\in Z[X_1,X_2,\dots]\) as a homogeneous basis indexed by these. For \(u,v\in S_\infty\), the product \(S_uS_v= \Sigma_w c^w_{uv}\) \((w\in S_\infty)\) where the structure ...
Bergeron, N, Sottile, F
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Structure theorems for braided Hopf algebras
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
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THE WELL-ORDERING OF DUAL BRAID MONOID
Journal of Knot Theory and Its Ramifications, 2010 We describe the restriction of the Dehornoy ordering of braids to the dual braid monoids introduced by Birman, Ko and Lee: we give an inductive characterization of the ordering of the dual braid monoids and compute the corresponding ordinal type. The proof consists in introducing a new ordering on the dual braid monoid using the rotating normal form ...
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Growth problems in diagram categories
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3454-3469, November 2025.Abstract In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
Jonathan Gruber, Daniel Tubbenhauer
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On Endomorphism Universality of Sparse Graph Classes
Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
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Pathological computations of Mackey functor‐valued Tor over cyclic groups
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3024-3036, October 2025.Abstract In equivariant algebra, Mackey functors play the role of abelian groups and Green and Tambara functors play the role of commutative rings. In this paper, we compute Mackey functor‐valued Tor over certain free Green and Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator.
David Mehrle +2 more
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A well-ordering of dual braid monoids [PDF]
Comptes Rendus. Mathématique, 2008 Let Bn+∗ denote the dual braid monoid on n strands, i.e., the submonoid of the braid group Bn consisting of the braids that can be expressed as positive words in the Birman–Ko–Lee generators. We introduce a new normal form on Bn+∗, which is based on expressing every braid of Bn+∗ in terms of a certain finite sequence of braids of Bn−1+∗.
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Mathematical Sciences and Applications E-Notes, 2021 Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. Let $\mathcal ODCT_{n}$ be the order-preserving and order-decreasing full contraction mappings on $X_{n}$. It is well known that $\mathcal ODCT_{n}$ is a monoid. In this paper, we have found the monoid rank and monoid presentation of $\mathcal ODCT_{n}$.
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