Results 21 to 30 of about 68,753 (202)
Kronecker coefficients: the tensor square conjecture and unimodality [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the $S_n$-irreducible representation indexed by the staircase partition
Igor Pak, Greta Panova, Ernesto Vallejo
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On the Irreducibility of the Krawtchouck Polynomials
, 2022 The Krawtchouck polynomials arise naturally in both coding theory and probability theory and have been studied extensively from these points of view. However, very little is known about their irreducibility and Galois properties. Just like many classical families of orthogonal polynomials (e.g.
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The Classification of All Singular Nonsymmetric Macdonald Polynomials
Axioms, 2022 The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys–Murphy elements whose simultaneous ...
Charles F. Dunkl
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Irreducible polynomials in Int(ℤ)
ITM Web of Conferences, 2018 In order to fully understand the factorization behavior of the ring Int(ℤ) = {f ∈ ℚ[x] | f (ℤ) ⊆ ℤ} of integer-valued polynomials on ℤ, it is crucial to identify the irreducible elements.
Antoniou Austin +2 more
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On the irreducible factors of a polynomial II [PDF]
Journal of Algebra, 2020 We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].
Anuj Jakhar, Kotyada Srinivas
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Necessary and sufficient conditions for the existence of invariant algebraic curves
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We present a set of conditions enabling a polynomial system of ordinary differential equations in the plane to have invariant algebraic curves. These conditions are necessary and sufficient. Our main tools include factorizations over the field of Puiseux
Maria Demina
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Combinatorial interpretation and positivity of Kerov's character polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Kerov's polynomials give irreducible character values of the symmetric group in term of the free cumulants of the associated Young diagram. Using a combinatorial approach with maps, we prove in this article a positivity result on their coefficients ...
Valentin Féray
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Computing low-degree factors of lacunary polynomials: a Newton-Puiseux approach [PDF]
, 2014 We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero.
Grenet, Bruno
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Современные информационные технологии и IT-образование, 2019 We consider vector mappings over the set of 0 and 1 given by the set of Boolean functions. Boolean functions included in the map are given in ANF. Having fixed the rule according to which the binary vectors are associated with the elements of a finite ...
Sergey A. Belov
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The Smallest Singular Values and Vector-Valued Jack Polynomials [PDF]
, 2018 There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials.
Dunkl, Charles F.
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