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TL;DR: A large class of predicates P is exhibited such that the monadic theory MTh?N, <, P?
Abstract: We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures ?N, <, P? which expand the ordering ?N,
56 citations
TL;DR: The algorithm introduced is explicit and it is proved that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation.
56 citations
TL;DR: In this article, the interpretation of the WSC time series is carried out by combining a backscattering model to a grassland growth model and the resolution of the inverse problem is based on a brute-force method that consists of exploring all the combinations of parameters of interest.
55 citations
TL;DR: In this paper, it was shown that the set of polynomials with positive upper Banach density is nonempty for some prime p. This generalizes earlier results of the authors of Wooley and Ziegler.
Abstract: If
$\vec q_1 ,...,\vec q_m $
: ℤ → ℤ
l
are polynomials with zero constant terms and E ⊂ ℤ
l
has positive upper Banach density, then we show that the set E ∩ (E −
$\vec q_1 $
(p − 1)) ∩ … ∩ (E −
$\vec q_m $
(p − 1)) is nonempty for some prime p. We also prove mean convergence for the associated averages along the prime numbers, conditional to analogous convergence results along the full integers. This generalizes earlier results of the authors, of Wooley and Ziegler, and of Bergelson, Leibman and Ziegler.
55 citations
Posted Content•
TL;DR: In this paper, a graded Hopf algebra based on the set of parking functions is introduced, which can be embedded into a noncommutative polynomial algebra in infinitely many variables, and admits natural quotients and subalgebras whose graded components have dimensions given by the Schroder numbers (plane trees), the Catalan numbers, and powers of 3.
Abstract: We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension (n+1)^{n-1} in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schroder numbers (plane trees), the Catalan numbers, and powers of 3.
These smaller algebras are always bialgebras and belong to some family of di- or tri-algebras occuring in the works of Loday and Ronco.
Moreover, the fundamental notion of parkization allows one to endow the set of parking functions of fixed length with an associative multiplication (different from the one coming from the Shi arrangement), leading to a generalization of the internal product of symmetric functions. Several of the intermediate algebras are stable under this operation. Among them, one finds the Solomon descent algebra but also a new algebra based on a Catalan set, admitting the Solomon algebra as a left ideal.
55 citations
Authors
Showing all 831 results
| Name | H-index | Papers | Citations |
|---|---|---|---|
| Dapeng Yu | 94 | 745 | 33613 |
| Daniel Azoulay | 78 | 510 | 23979 |
| Mehmet A. Oturan | 77 | 261 | 22682 |
| Alfred O. Hero | 73 | 899 | 29258 |
| Nihal Oturan | 64 | 174 | 12092 |
| Jean-Christophe Pesquet | 50 | 364 | 13264 |
| Eric D. van Hullebusch | 50 | 265 | 9030 |
| Christian Soize | 48 | 529 | 9932 |
| Maxime Crochemore | 47 | 314 | 9836 |
| Jean-Yves Thibon | 42 | 191 | 6398 |
| Marie-France Sagot | 41 | 191 | 5972 |
| François Farges | 41 | 111 | 6349 |
| Laurent Najman | 40 | 233 | 9238 |
| Renaud Keriven | 39 | 108 | 6330 |
| Robert Eymard | 39 | 171 | 6964 |