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Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees
We obtain a polynomial upper bound in the finite-field version of the multidimensional polynomial Szemerédi theorem for distinct-degree polynomials....
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Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in Mrozek (Found Comput Math 17(6):1585–1633,...
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Multi-dimensional constacyclic codes of arbitrary length over finite fields
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over...
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Combinatorics of Euclidean Spaces over Finite Fields
The q -binomial coefficients are q -analogues of the binomial coefficients, counting the number of k -dimensional subspaces in the n -dimensional vector...
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Construction methods for Galois LCD codes over finite fields
In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several...
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Induced arithmetic removal: complexity 1 patterns over finite fields
We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that...
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Exponential Sums over Finite Fields
This is an expository paper on algebraic aspects of exponential sums over finite fields. This is a new direction. Various examples, results and open...
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Periodic Groups Saturated with Finite Simple Symplectic Groups of Dimension 6 over Fields of Odd Characteristics
We prove that a periodic group is locally finite, if its every finite subgroup lies in a subgroup isomorphic to a simple symplectic group of...
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Affine connection, quantum theory and new fields
In a few recent manuscripts, we used the affine connection to introduce two massless scalar fields in the Einstein-Palatini action. These fields lead...
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Measures on perfect e-free PAC fields
We construct measures on definable sets in e -free perfect PAC fields, as well as on perfect PAC fields whose absolute Galois groups are free pro- p of...
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Fields, Division Rings
Using basic properties of finite cyclic groups, we shall prove the following property.
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Occupation Fields
Occupation fields of loop ensembles for vertices and oriented edges are introduced and their distributions are computed, together with the variations...