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Computational complexity in algebraic combinatorics

Current Developments in Mathematics
Notes associated with the Current Developments in Mathematics 2023 ...
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CODING THEORY AND ALGEBRAIC COMBINATORICS [PDF]

, 2010
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes.
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Homogeneous Algebras, Statistics and Combinatorics

Letters in Mathematical Physics, 2002
After some generalities on homogeneous algebras, we give a formula connecting the Poincaré series of a homogeneous algebra with the homology of the corresponding Koszul complex generalizing thereby a standard result for quadratic algebras. We then investigate two particular types of cubic algebras: The first one called the parafermionic (parabosonic ...
Dubois-Violette, Michel, Popov, Todor
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PENINGKATAN KOMPETENSI GURU PEMBINA OLIMPIADE MATEMATIKA SISWA SEKOLAH MENENGAH PERTAMA KABUPATEN MADIUN

As-Sidanah, 2019
The objective of this research is to describe the improvement of the competence of Olympic workshop participants in problem-solving of mathematics Olympiad for mathematics teachers of Junior High Schools in the Madiun Regency by using the qualitative ...
Mohammad Tohir
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Combinatorics of free vertex algebras [PDF]

Journal of Algebra, 2002
This paper illustrates the combinatorial approach to vertex algebra - study of vertex algebras presented by generators and relations. A necessary ingredient of this method is the notion of free vertex algebra. Borcherds \cite{bor} was the first to note that free vertex algebras do not exist in general. The reason for this is that vertex algebras do not
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Further results on permanents of Laplacian matrices of trees

Open Mathematics
The research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees.
Wu Tingzeng, Dong Xiangshuai
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Some applications of algebra to combinatorics

Discrete Applied Mathematics, 1991
The author gives a very interesting survey of the application of algebraic methods in combinatorics, in the setting of (graded) partially ordered sets and lattices. Major themes are provided by the Sperner property, rank symmetry and rank unimodality. The algebraic methods employed range from linear algebra via group actions to Lie algebras.
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Cubic surfaces and their invariants: Some memories of Raymond Stora

Nuclear Physics B, 2016
Cubic surfaces embedded in complex projective 3-space are a classical illustration of the use of old and new methods in algebraic geometry. Recently, they made their appearance in physics, and in particular aroused the interest of Raymond Stora, to the ...
Michel Bauer
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Δ–Springer varieties and Hall–Littlewood polynomials

Forum of Mathematics, Sigma
The $\Delta $ -Springer varieties are a generalization of Springer fibers introduced by Levinson, Woo and the author that have connections to the Delta Conjecture from algebraic combinatorics.
Sean T. Griffin
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Binomial Cayley graphs and applications to dynamics on finite spaces [PDF]

Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the other with ...
Viganò, Francesco, Bassols Cornudella, Bernat   +1 more
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