Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Koutschan, Christoph"'
Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear functions
Externí odkaz:
http://arxiv.org/abs/2406.02421
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for proving and disc
Externí odkaz:
http://arxiv.org/abs/2405.02430
Publikováno v:
J. Symbol. Comput. 127 (2025), 102352
In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the e
Externí odkaz:
http://arxiv.org/abs/2401.08481
The enumeration of diagonally symmetric alternating sign matrices (DSASMs) is studied, and a Pfaffian formula is obtained for the number of DSASMs of any fixed size, where the entries for the Pfaffian are positive integers given by simple binomial co
Externí odkaz:
http://arxiv.org/abs/2309.08446
Autor:
Amdeberhan, Tewodros, Moll, Victor, Santander, John Lopez, McLaughlin, Ken, Koutschan, Christoph
The long-time behavior of solutions to the initial value problem for the Korteweg-de Vries equation on the whole line, with general initial conditions has been described uniformly using five different asymptotic forms. Four of these asymptotic forms
Externí odkaz:
http://arxiv.org/abs/2309.02925
Publikováno v:
A case study in determinant evaluations, S\'eminaire Lotharingien de Combinatoire, 89 (2023), Article B89a
In this {\it case study}, we hope to show why Sheldon Axler was not just wrong, but {\em wrong}, when he urged, in 1995: ``Down with Determinants!''. We first recall how determinants are useful in enumerative combinatorics, and then illustrate three
Externí odkaz:
http://arxiv.org/abs/2307.01912
A piecewise linear function can be described in different forms: as an arbitrarily nested expression of $\min$- and $\max$-functions, as a difference of two convex piecewise linear functions, or as a linear combination of maxima of affine-linear func
Externí odkaz:
http://arxiv.org/abs/2305.16933
Autor:
Kauers, Manuel, Koutschan, Christoph
Publikováno v:
Journal of Integer Sequences, vol. 26, article 23.4.5, 2023
In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite. In some cases, we are able to prove the conjectured recurrence. In some cases, we are not able to prove the
Externí odkaz:
http://arxiv.org/abs/2303.02793
We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study analytical m
Externí odkaz:
http://arxiv.org/abs/2303.02560
Publikováno v:
Proceedings of International Symposium on Symbolic and Algebraic Computation 2023
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we pr
Externí odkaz:
http://arxiv.org/abs/2302.06396