Results 11 to 20 of about 56,399 (238)
Polynomial solutions of binomial congruences [PDF]
Journal of the Australian Mathematical Society, 1960 Polynomial solutions of a few binomial congruences have been known for a long time. For instance Legendre showed that the congruence has a solution this being the expansion of as far as the term of degree m — 3. [1] It seems that only restricted types, e.g. (1), have been investigated.
H. Lindgren
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The binomial formula for nonsymmetric Macdonald polynomials
Duke Mathematical Journal, 1997 Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beautiful expansion formula which can be viewed as a multivariable generalization of the q-binomial theorem.
Siddhartha Sahi
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Computing the binomial part of a polynomial ideal
Journal of Symbolic Computation, 2023 Given an ideal $I$ in a polynomial ring $K[x_1,\dots,x_n]$ over a field $K$, we present a complete algorithm to compute the binomial part of $I$, i.e., the subideal ${\rm Bin}(I)$ of $I$ generated by all monomials and binomials in $I$. This is achieved step-by-step.
Martin Kreuzer, Florian Walsh
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Absolute irreducibility of the binomial polynomials [PDF]
Journal of Algebra, 2021 In this paper we investigate the factorization behaviour of the binomial polynomials $\binom{x}{n} = \frac{x(x-1)\cdots (x-n+1)}{n!}$ and their powers in the ring of integer-valued polynomials $\operatorname{Int}(\mathbb{Z})$. While it is well-known that the binomial polynomials are irreducible elements in $\operatorname{Int}(\mathbb{Z})$, the ...
Roswitha Rissner, Daniel Windisch
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Zeros of a binomial combination of Chebyshev polynomials [PDF]
International Journal of Number Theory, 2020 For [Formula: see text], we study the zeros of the sequence of polynomials [Formula: see text] generated by the reciprocal of [Formula: see text], expanded as a power series in [Formula: see text]. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number
Summer Al Hamdani, Khang Tran
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New Class of Quantum Error-Correcting Codes for a Bosonic Mode
Physical Review X, 2016 We construct a new class of quantum error-correcting codes for a bosonic mode, which are advantageous for applications in quantum memories, communication, and scalable computation.
Marios H. Michael +6 more
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Binomial formula for Macdonald polynomials
, 1996 AMS TeX, 20 pages. Replaced with journal version. To appear in Math.
Andreĭ Okounkov
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Binomial Eulerian polynomials for colored permutations [PDF]
Journal of Combinatorial Theory, Series A, 2020 Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and Williams on the face enumeration of generalized permutohedra. They are $ $-positive (in particular, palindromic and unimodal) polynomials which can be interpreted as $h$-polynomials of certain flag simplicial polytopes and which admit interesting Schur $ $-positive ...
Christos A. Athanasiadis
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Regularity and h-polynomials of binomial edge ideals [PDF]
Acta Mathematica Vietnamica, 2018 6 pages. Conjecture 0.1 has been deleted.
Takayuki Hibi, Kazunori Matsuda
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GENERALIZED BINOMIAL EXPANSIONS AND BERNOULLI POLYNOMIALS
, 2014 We investigate generalized binomial expansions that arise from two-dimensional sequences satisfying a broad generalization of the triangular recurrence for binomial coefficients. In particular, we present a new combinatorial formula for such sequences in terms of a 'shift by rank' quasi-expansion based on ordered set partitions.
Hiêú D. Nguyêñ
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