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Journal articles on the topic 'Polynômes caractéristiques'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Chabert, Jean-Luc, and Gilbert Gerboud. "Polynômes à Valeurs Entières Et Binômes De Fermat." Canadian Journal of Mathematics 45, no. 1 (1993): 6–21. http://dx.doi.org/10.4153/cjm-1993-002-8.

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RésuméSoit A un anneau intègre de corps des fractions K et soit A[X]sub = {P(X) ∈ K[X] ; P(ℤ) ⊂ A} l'anneau des polynômes à valeurs entières sur A. Lorsque la caractéristique de A est nulle, le A-module A[X]sub est contenu dans le A-module {P(X) ∊ K[X] ; P(Z) ⊂ A] engendré par les polynômes binomiaux Bn(X) – X(X – 1) (X – n + 1)/n′. Nous caractérisons ici les anneaux de Dedekind A pour lesquels ces A-modules sont égaux.Puis nous étudions la situation plus générale dans laquelle A[X]sub = {P(X) ∈ K[X] ; P(A0) ⊂ A} OÙ A0 désigne un anneau de Dedekind contenu dans A. Ce sont alors des polynômes g

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2

Poizat, Bruno. "Une dualité entre fonctions booléennes." Journal of the Institute of Mathematics of Jussieu 9, no. 3 (2010): 633–52. http://dx.doi.org/10.1017/s1474748010000083.

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RésuméSi k est un corps fini, toute fonction f(x1, … , xm) de {0, 1}m dans k s'écrit de manière unique comme un polynôme, à coefficients dans k, de degré un ou zéro en chacune de ses variables ; on peut donc lui associer une fonction f*(x1, … , xm), sa duale inverse, qui exprime les coefficients de son polynôme canonique. Nous considérons l'improbable hypothèse que la classe P(k), formée des suites de fonctions calculables en un nombre d'opérations (additions et multiplications) de croissance polynomialement bornée, soit close par dualité ; nous montrons qu'elle équivaut à une hypothèse bien c

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3

Portier, Natacha. "Le problème des grandes puissances et celui des grandes racines." Journal of Symbolic Logic 65, no. 4 (2000): 1675–85. http://dx.doi.org/10.2307/2695068.

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RésuméSoit f une fonction de N dans N qui ne soit pas calculable en temps polynomial, et a un élément d'un corps differentiel K de caractéristique nulle. Nous appelons probleme des grandes puissances l'ensembledes uples = (x1…..xn) de K telsque x1 = af(n) et problème des grandes racines l'ensemble des uples de K tels que . Ce sont deux exemples de problèmes que l'utilisation de la dérivée ne permet pas de résoudre plus rapidement. Nous montrons que le problème des grandes racines n'est pas polynomial au sens des corps differentiels, même si nous autorisons un nombre polynomial de paramètres. e

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4

Adam, David. "Polynômes à valeurs entières ainsi que leurs dérivées en caractéristique p." Acta Arithmetica 148, no. 4 (2011): 351–65. http://dx.doi.org/10.4064/aa148-4-3.

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5

Dehaye, Paul-Olivier. "A note on moments of derivatives of characteristic polynomials." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2823.

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International audience We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to compute matrix averages of characteristic polynomials. In order to consider derivatives of those polynomials, we here need the added strength of the Generalized Binomial Theorem of Okounkov and Olshanski. This result is very natural as it provides coefficients for the Taylor expansions of Schur functions, in terms of shifted Schur funct

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6

Delcroix-Oger, Bérénice. "Semi-pointed partition posets." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (2015). http://dx.doi.org/10.46298/dmtcs.2532.

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International audience We present here a family of posets which generalizes both partition and pointed partition posets. After a short description of these new posets, we show that they are Cohen-Macaulay, compute their Moebius numbers and their characteristic polynomials. The characteristic polynomials are obtained using a combinatorial interpretation of the incidence Hopf algebra associated to these posets. Nous introduisons ici une famille de posets qui généralise à la fois les poset de partitions et les posets de partitions pointées. Après une description rapide de ces nouveaux posets, nou

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7

Moci, Luca. "Zonotopes, toric arrangements, and generalized Tutte polynomials." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2878.

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International audience We introduce a multiplicity Tutte polynomial $M(x,y)$, which generalizes the ordinary one and has applications to zonotopes and toric arrangements. We prove that $M(x,y)$ satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial $M(x,y)$, likewise the corresponding polynomials for a hyperplane arrangement are specializations of the ordinary Tutte polynomial. Furthermore, $M(1,y)$ is the Hilbert series of the relate

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8

Lenz, Matthias. "Hierarchical Zonotopal Power Ideals." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (2011). http://dx.doi.org/10.46298/dmtcs.2939.

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International audience Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors. Given such a sequence $X$, an integer $k \geq -1$ and an upper set in the lattice of flats of the matroid defined by $X$, we define and study the associated $\textit{hierarchical zonotopal power ideal}$. This ideal is generated by powers of linear forms. Its Hilbert series depends only on the matroid structure of $X$. It is related to various other matroid invariants, $\textit{e. g.}$ the shelling

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9

Khouya, Ahmed, and Abdeslam Draoui. "Détermination des courbes caractéristiques de séchage de trois espèces de bois." Journal of Renewable Energies 12, no. 1 (2023). http://dx.doi.org/10.54966/jreen.v12i1.122.

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Le séchage est un processus incontournable de la transformation du bois en produits finis, qui se doit d’être optimisé en fonction des critères qualité, temps et coût. Ce processus a pour objectif de diminuer le plus rapidement possible l’humidité du bois tout en limitant au minimum les pertes éventuelles de qualité (gerces, tensions internes.). Ainsi la connaissance du comportement des structures en bois dans différentes conditions d’environnement est parmi les conditions essentielles pour l’exploitation de ce matériau. Pour valoriser le matériau bois, notre étude consiste à déterminer la cou

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10

Blandin, Héctor. "Generalized Polarization Modules (extended abstract)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (2015). http://dx.doi.org/10.46298/dmtcs.2456.

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International audience This work enrols the research line of M. Haiman on the Operator Theorem (the old operator conjecture). This theorem states that the smallest $\mathfrak{S}_n$-module closed under taking partial derivatives and closed under the action of polarization operators that contains the Vandermonde determinant is the space of diagonal harmonics polynomials. We start generalizing the context of this theorem to the context of polynomials in $\ell$ sets of $n$ variables $x_{ij}$ with $1\le i \le \ell$ and $1 \le j \le n$. Given a $\mathfrak{S}_n$-stable family of homogeneous polynomia

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11

Sam, Steven V. "Schubert complexes and degeneracy loci." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2831.

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International audience The classical Thom―Porteous formula expresses the homology class of the degeneracy locus of a generic map between two vector bundles as an alternating sum of Schur polynomials. A proof of this formula was given by Pragacz by expressing this alternating sum as the Euler characteristic of a Schur complex, which gives an explanation for the signs. Fulton later generalized this formula to the situation of flags of vector bundles by using alternating sums of Schubert polynomials. Building on the Schubert functors of Kraśkiewicz and Pragacz, we introduce Schubert complexes and

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12

Can, Mahir Bilen. "Nested Hilbert Schemes and the nested $q,t$-Catalan series." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AJ,..., Proceedings (2008). http://dx.doi.org/10.46298/dmtcs.3636.

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International audience In this paper we study the tangent spaces of the smooth nested Hilbert scheme $\mathrm{Hilb}^{n,n-1}(\mathbb{A}^2)$ of points in the plane, and give a general formula for computing the Euler characteristic of a $\mathbb{T}^2$-equivariant locally free sheaf on $\mathrm{Hilb}^{n,n-1}(\mathbb{A}^2)$. Applying our result to a particular sheaf, we conjecture that the result is a polynomial in the variables $q$ and $t$ with non-negative integer coefficients. We call this conjecturally positive polynomial as the "nested $q,t$-Catalan series,'' for it has many conjectural proper

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13

Kallipoliti, Myrto. "The absolute order on the hyperoctahedral group." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (2009). http://dx.doi.org/10.46298/dmtcs.2689.

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International audience The absolute order on the hyperoctahedral group $B_n$ is investigated. It is shown that every closed interval in this order is shellable, those closed intervals which are lattices are characterized and their zeta polynomials are computed. Moreover, using the notion of strong constructibility, it is proved that the order ideal generated by the Coxeter elements of $B_n$ is homotopy Cohen-Macaulay and the Euler characteristic of the order complex of the proper part of this ideal is computed. Finally, an example of a non Cohen-Macaulay closed interval in the absolute order o

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14

Derksen, Harm, and Alex Fink. "Valuative invariants for polymatroids." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2849.

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International audience Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant $\mathcal{G}$ introduced by the first author, are valuative. In this paper we construct the $\mathbb{Z}$-modules of all $\mathbb{Z}$-valued valuative functions for labelled matroids and polymatroids on a fixed ground set, and their unlabelled counterparts, the $\mathbb{Z}$-modules of valuative invariants. We give explicit bases for these modules and for their dual modules generated by indicator functions of polytopes, a

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15

Aguiar, Marcelo, and Aaron Lauve. "Convolution Powers of the Identity." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (2013). http://dx.doi.org/10.46298/dmtcs.2365.

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International audience We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and multiplicity - for the action of the operator $\mathtt{id}^{\ast n}$ on each homogeneous component $H_m$. The multiplicities are independent of $n$. This follows from considering the action of the (higher) Eulerian idempotents on a certain Lie algebra $\mathfrak{g}$ associated to $H$. In case $H$ is cofree, we give an alternative (e

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16

Armstrong, Drew, and Brendon Rhoades. "The Shi arrangement and the Ish arrangement." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (2011). http://dx.doi.org/10.46298/dmtcs.2890.

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International audience This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. The second — the Ish arrangement — was recently defined by the first author who used the two arrangements together to give a new interpretation of the q,t-Catalan numbers of Garsia and Haiman. In the present paper we will define a mysterious "combinatorial symmetry'' between the two arrangements and show that this symmetry preserves a great deal of information. For example, the Shi a

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17

Rundell, Sarah C., and Jane H. Long. "The Hodge Structure of the Coloring Complex of a Hypergraph (Extended Abstract)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2830.

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International audience Let $G$ be a simple graph with $n$ vertices. The coloring complex$ Δ (G)$ was defined by Steingrímsson, and the homology of $Δ (G)$ was shown to be nonzero only in dimension $n-3$ by Jonsson. Hanlon recently showed that the Eulerian idempotents provide a decomposition of the homology group $H_{n-3}(Δ (G))$ where the dimension of the $j^th$ component in the decomposition, $H_{n-3}^{(j)}(Δ (G))$, equals the absolute value of the coefficient of $λ ^j$ in the chromatic polynomial of $G, _{\mathcal{χg}}(λ )$. Let $H$ be a hypergraph with $n$ vertices. In this paper, we define

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