Results 71 to 80 of about 4,202,174 (239)
A coboundary Temperley–Lieb category for sl2$\mathfrak {sl}_{2}$‐crystals
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract By considering a suitable renormalization of the Temperley–Lieb category, we study its specialization to the case q=0$q=0$. Unlike the q≠0$q\ne 0$ case, the obtained monoidal category, TL0(k)$\mathcal {TL}_0(\mathbb {k})$, is not rigid or braided. We provide a closed formula for the Jones–Wenzl projectors in TL0(k)$\mathcal {TL}_0(\mathbb {k})$
Moaaz Alqady, Mateusz Stroiński
wiley +1 more source
Congruence preserving functions on free monoids [PDF]
Algebra universalis, 2017 A function on an algebra is congruence preserving if, for any congruence, it maps congruent elements to congruent elements. We show that, on a free monoid generated by at least 3 letters, a function from the free monoid into itself is congruence preserving %nonmonogenic if and only if it is of the form $x \mapsto w_0 x w_1 \cdots w_{n-1} x w_n$ for ...
Cégielski, Patrick +2 more
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G$G$‐typical Witt vectors with coefficients and the norm
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract For a profinite group G$G$ we describe an abelian group WG(R;M)$W_G(R; M)$ of G$G$‐typical Witt vectors with coefficients in an R$R$‐module M$M$ (where R$R$ is a commutative ring). This simultaneously generalises the ring WG(R)$W_G(R)$ of Dress and Siebeneicher and the Witt vectors with coefficients W(R;M)$W(R; M)$ of Dotto, Krause, Nikolaus ...
Thomas Read
wiley +1 more source
Homogeneous braids are visually prime
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent interest.
Peter Feller +2 more
wiley +1 more source
On the rank of the subsets of a free monoid
Theoretical Computer Science, 1992 For a subset \(X \subseteq A^*\) of a word monoid \(A^*\), the rank of \(X\) is defined to be the minimal cardinality \(r(X)\) of a set \(Y\) such that \(X \subset Y^*\). By the defect theorem \(r(X) < | X|\) if \(X^*\) is not a free monoid. The author studies how the rank function behaves with respect to the operations of union, intersection ...
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Monogenic endomorphisms of a free monoid [PDF]
Glasgow Mathematical Journal, 1989 Free monoids play a central role in the theory of formal languages. Their endomorphisms appear naturally in the context of deterministic OL-schemes which trace their origin to biology. Closely related to such a scheme is a DOL-system which consists of a triple (X, φ, w) where X is a finite set, φ is an endomorphism of the free monoid X* and w ∈ X.
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Coloured shuffle compatibility, Hadamard products, and ask zeta functions
Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 2132-2154, July 2025.Abstract We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so‐called ask zeta functions of direct sums of modules of matrices or class‐ and orbit‐counting zeta functions of direct products of nilpotent groups.
Angela Carnevale +2 more
wiley +1 more source
Moduli of finite flat torsors over nodal curves
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract We show that log flat torsors over a family X/S$X/S$ of nodal curves under a finite flat commutative group scheme G/S$G/S$ are classified by maps from the Cartier dual of G$G$ to the log Jacobian of X$X$. We deduce that fppf torsors on the smooth fiberss of X/S$X/S$ can be extended to global log flat torsors under some regularity hypotheses.
Sara Mehidi, Thibault Poiret
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Homotopical commutative rings and bispans
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We prove that commutative semirings in a cartesian closed presentable ∞$\infty$‐category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product‐preserving functors from the (2,1)‐category of bispans of finite sets. In other words, we identify the latter as the Lawvere theory for commutative semirings in the ∞$\infty$‐categorical
Bastiaan Cnossen +3 more
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The homomorphism problem for the free monoid
Discrete Mathematics, 2002 The following extension problem for mappings is shown to be algorithmically decidable: given a finite subset \(F\) of words over an alphabet \(X\) and a mapping \(\varphi\colon F\to X^*\), determine whether or not \(\varphi\) can be extended to a monoid homomorphism \(F^*\to X^*\).
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