Zobrazeno 1 - 10
of 217
pro vyhledávání: '"Koutschan, Christoph"'
A chessboard has the property that every row and every column has as many white squares as black squares. In this mostly methodological note, we address the problem of counting such rectangular arrays with a fixed (numeric) number of rows, but an arb
Externí odkaz:
http://arxiv.org/abs/2410.07435
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