Results 11 to 20 of about 69 (69)
Homogeneous algebras, statistics and combinatorics
Letters in Mathematical Physics, 2002 After some generalities on homogeneous algebras, we give a formula connecting the Poincar 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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COMBINATORICS OF ULTRAFILTERS ON COHEN AND RANDOM ALGEBRAS [PDF]
The Journal of Symbolic Logic, 2021 AbstractWe investigate the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. In particular, this paper provides several techniques to construct ultrafilters which are not Tukey maximal. Furthermore, we connect this analysis with a cardinal invariant of Boolean algebras, the ultrafilter number, and prove consistency ...
Brendle J., Parente F.
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COMBINATORICS AND N-KOSZUL ALGEBRAS [PDF]
International Journal of Geometric Methods in Modern Physics, 2008 The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables.
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Recent progress in algebraic combinatorics [PDF]
Bulletin of the American Mathematical Society, 2002 We survey three recent breakthroughs in algebraic combinatorics. The first is the proof by Knutson and Tao, and later Derksen and Weyman, of the saturation conjecture for Littlewood-Richardson coefficients. The second is the proof of then!n!and(n+1)n−1(n+1)^{n-1}conjectures by Haiman.
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European Journal of Combinatorics, 2010 The present issue of Designs, Codes and Cryptography is devoted to the theme “Geometric and Algebraic Combinatorics”. A central concept in this research area is the Association Scheme. On one hand it can be a tool for a better understanding of combinatorial objects, such as error correcting codes, block designs, point-line incidence geometries, and ...
Edwin van Dam, Willem H. Haemers
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Weighted Turán Theorems With Applications to Ramsey‐Turán Type of Problems
Journal of Graph Theory, EarlyView.ABSTRACT We study extensions of Turán Theorem in edge‐weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey‐Turán type problems.
József Balogh +2 more
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Combinatorics and the Schur algebra
Journal of Pure and Applied Algebra, 1993 The structure of the Schur algebra SR(n, r) over an arbitrary commutative ring R is studied by a method based on the theorem of Mead, Rota and others, which gives a basis of bideterminants for the R-module AR(n, r) of all homogeneous polynomials of degree r in n2 indeterminates over R. It is shown that SR(n, r) has an analogous basis of codeterminants,
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad +1 more
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On the combinatorics of commutators of Lie algebras [PDF]
Journal of Algebra and Its Applications, 2019 Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator [Formula: see text] as a sum of associative monomials. We characterize this subset and find some useful equivalences.
Eduardo Eizo Aramaki Hitomi +1 more
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On Generalized Avicenna Numbers
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Avicenna numbers that we define in this paper, are a class of figurate numbers, including icosahedral, octahedral, tetrahedral, dodecahedral, rhombicosidodecahedral numbers and cubes, play a key role in mathematics, physics and various scientific fields.
Melih Göcen, Yüksel Soykan
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