Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Chyzak, Frederic"'
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
We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on $\mathbb{Z}^2$ defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or $-1$. We concern ourselves with the enume
Externí odkaz:
http://arxiv.org/abs/1606.02982