Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Chyzak, Frédéric"'
Autor:
Chyzak, Frédéric, Mishna, Marni
By a classic result of Gessel, the exponential generating functions for $k$-regular graphs are D-finite. Using Gr\"obner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regu
Externí odkaz:
http://arxiv.org/abs/2406.04753
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators$\ell_r M^r + \dots + \ell_1 M + \ell_0$where $\ell_0, \dots, \ell_r$ are polynomials in~$x$ and $Mx = x^b M$ for some integer $b
Externí odkaz:
http://arxiv.org/abs/2403.11545
We provide short product formulas for the $f$-vectors of the canonical complexes of the Tamari lattices and of the cellular diagonals of the associahedra.
Comment: 38 pages, 8 figures, 15 tables. Version 3: New Section 5 on binomial sums
Comment: 38 pages, 8 figures, 15 tables. Version 3: New Section 5 on binomial sums
Externí odkaz:
http://arxiv.org/abs/2303.10986
We present a symbolic-numeric Las Vegas algorithm for factoring Fuchsian ordinary differential operators with rational function coefficients. The new algorithm combines ideas of van Hoeij's "local-to-global" method and of the ''analytic'' approach pr
Externí odkaz:
http://arxiv.org/abs/2205.08991
Autor:
Chyzak, Frédéric, Nielsen, Frank
We report a closed-form expression for the Kullback-Leibler divergence between Cauchy distributions which involves the calculation of a novel definite integral. The formula shows that the Kullback-Leibler divergence between Cauchy densities is always
Externí odkaz:
http://arxiv.org/abs/1905.10965
Autor:
Chyzak, Frédéric, Yeats, Karen
In this article, we study the enumeration by length of several walk models on the square lattice. We obtain bijections between walks in the upper half-plane returning to the $x$-axis and walks in the quarter plane. A recent work by Bostan, Chyzak, an
Externí odkaz:
http://arxiv.org/abs/1810.04117
Publikováno v:
Proceedings of ISSAC 2018 (New York, NY, USA)
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite reduction to arbi
Externí odkaz:
http://arxiv.org/abs/1805.03445
In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coeffi
Externí odkaz:
http://arxiv.org/abs/1802.08653
Publikováno v:
Mathematics of Computation, 87 (2018), 2977-3021
Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently, the problem
Externí odkaz:
http://arxiv.org/abs/1612.05518
Autor:
Chyzak, Frédéric
Le télescopage créatif est un principe algorithmique développé depuis les années 1990 en combinatoire et en calcul formel, notamment depuis les travaux de Doron Zeilberger, pour calculer avec des sommes et intégrales paramétrées, que ce soit
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-01069831
http://tel.archives-ouvertes.fr/docs/01/06/98/31/PDF/h.pdf
http://tel.archives-ouvertes.fr/docs/01/06/98/31/PDF/h.pdf