Results 41 to 50 of about 69 (69)
Lattices in function fields and applications
Mathematika, Volume 71, Issue 2, April 2025.Abstract In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields.
Christian Bagshaw, Bryce Kerr
wiley +1 more source
A sharp higher order Sobolev embedding
Mathematika, Volume 71, Issue 2, April 2025.Abstract We obtain sharp embeddings from the Sobolev space W0k,2(−1,1)$W^{k,2}_0(-1,1)$ into the space L1(−1,1)$L^1(-1,1)$ and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin.
Raul Hindov +3 more
wiley +1 more source
Physics, Combinatorics and Hopf Algebras
, 2004 A number of problems in theoretical physics share a common nucleus of combinatoric nature. It is argued here that Hopf algebraic concepts and techiques can be particularly efficient in dealing with such problems. As a first example, a brief review is given of the recent work of Connes, Kreimer and collaborators on the algebraic structure of the process
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Blow-up algebras in Algebra, Geometry and Combinatorics
, 2019 Programa de Doctorat en Matemàtica i ...
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HIGHER ALGEBRA IN COMBINATORICS
, 2023 This article has easy and a very nice application on how to solve elementary combinatorics problems using linear ...
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Problems in Algebraic Combinatorics
The Electronic Journal of Combinatorics, 1995 This is a list of open problems, mainly in graph theory and all with an algebraic flavour. Except for 6.1, 7.1 and 12.2 they are either folklore, or are stolen from other people.
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Operads in algebraic combinatorics
, 2017 The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying algebraically the structures thus obtained (changes of bases, generating sets, presentations, morphisms ...
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Combinatorics of rooted trees and Hopf algebras [PDF]
Transactions of the American Mathematical Society, 2003 We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the operator that multiplies a rooted tree by its number of ...
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Algebraic and Geometric Methods in Enumerative Combinatorics [PDF]
, 2015 A survey written for the upcoming "Handbook of Enumerative Combinatorics".
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Some applications of algebra to combinatorics
Discrete Applied Mathematics, 1991 Stanley, R.P., Some applications of algebra to combinatorics, Discrete Applied Mathematics 34 (1991) 241-277.
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