Philippe Nadeau
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View article: The quasisymmetric flag variety: a toric complex on noncrossing partitions
The quasisymmetric flag variety: a toric complex on noncrossing partitions Open
We develop the geometric theory of equivariant quasisymmetry via a new ``quasisymmetric flag variety''. This is a toric complex in the flag variety whose fixed point set is the set of noncrossing partitions, and whose cohomology ring is th…
View article: Algebraic combinatorics around a problem in enumerative geometry
Algebraic combinatorics around a problem in enumerative geometry Open
The research presented in this habilitation thesis falls within the field of algebraic combinatorics, and consists of several original contributions. It was initially motivated by an enumerative geometry problem: namely, the explicit compu…
View article: Equivariant quasisymmetry and noncrossing partitions
Equivariant quasisymmetry and noncrossing partitions Open
We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of double Schur and double Schubert polynomials that we call …
View article: Schubert polynomial expansions revisited
Schubert polynomial expansions revisited Open
We give an elementary approach utilizing only the divided difference formalism for obtaining expansions of Schubert polynomials that are manifestly nonnegative, by studying solutions to the equation $\sum Y_i\partial _i=\operatorname {id}$…
View article: The geometry of quasisymmetric coinvariants
The geometry of quasisymmetric coinvariants Open
We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric interpre…
View article: \(P\)-partitions with flags and back stable quasisymmetric functions
\(P\)-partitions with flags and back stable quasisymmetric functions Open
Stanley's theory of \\((P,\\omega)\\)-partitions is a standard tool in combinatorics. It can be extended to allow for the presence of a restriction, that is a given maximal value for partitions at each vertex of the poset, as was shown by …
View article: Quasisymmetric divided differences
Quasisymmetric divided differences Open
We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials and the associated divided difference operators. Our counterparts are "forest polynomials", and a new family of linear operators, whose theory of comp…
View article: Koszulity of dual braid monoid algebras via cluster complexes
Koszulity of dual braid monoid algebras via cluster complexes Open
The dual braid monoid was introduced by Bessis in his work on complex reflection arrangements. The goal of this work is to show that Koszul duality provides a nice interplay between the dual braid monoid and the cluster complex introduced …
View article: Automated Continuous Force-Torque Sensor Bias Estimation
Automated Continuous Force-Torque Sensor Bias Estimation Open
Six axis force-torque sensors are commonly attached to the wrist of serial robots to measure the external forces and torques acting on the robot's end-effector. These measurements are used for load identification, contact detection, and hu…
View article: Wiener Indices of Minuscule Lattices
Wiener Indices of Minuscule Lattices Open
The Wiener index of a finite graph $G$ is the sum over all pairs $(p,q)$ of vertices of $G$ of the distance between $p$ and $q$. When $P$ is a finite poset, we define its Wiener index as the Wiener index of the graph of its Hasse diagram. …
View article: Tamari intervals and blossoming trees
Tamari intervals and blossoming trees Open
We introduce a simple bijection between Tamari intervals and the blossoming trees (Poulalhon and Schaeffer, 2006) encoding planar triangulations, using a new meandering representation of such trees. Its specializations to the families of s…
View article: Smirnov words and the Delta Conjectures
Smirnov words and the Delta Conjectures Open
We provide a combinatorial interpretation of the symmetric function $\left.Θ_{e_k}Θ_{e_l}\nabla e_{n-k-l}\right|_{t=0}$ in terms of segmented Smirnov words. The motivation for this work is the study of a diagonal coinvariant ring with one …
View article: Precision measurement of the specific activity of $$^{39}$$Ar in atmospheric argon with the DEAP-3600 detector
Precision measurement of the specific activity of $$^{39}$$Ar in atmospheric argon with the DEAP-3600 detector Open
The specific activity of the $$\beta $$ decay of $$^{39}$$ Ar in atmospheric argon is measured using the DEAP-3600 detector. DEAP-3600, located 2 km underground at SNOLAB, uses a total of (3269 ± 24) kg of liquid argon distilled from …
View article: $[\text{Perm}_n]$ via $\text{QSym}_n^+$
$[\text{Perm}_n]$ via $\text{QSym}_n^+$ Open
International audience
View article: Forest polynomials and the class of the permutahedral variety
Forest polynomials and the class of the permutahedral variety Open
We study a basis of the polynomial ring that we call forest polynomials. This family of polynomials is indexed by a combinatorial structure called indexed forests and permits several definitions, one of which involves flagged P-partitions.…
View article: $P$-partitions with flags and back stable quasisymmetric functions
$P$-partitions with flags and back stable quasisymmetric functions Open
Stanley's theory of $(P,ω)$-partitions is a standard tool in combinatorics. It can be extended to allow for the presence of a restriction, that is a given maximal value for partitions at each vertex of the poset, as was shown by Assaf and …
View article: Precision Measurement of the Specific Activity of $^{39}$Ar in Atmospheric Argon with the DEAP-3600 Detector
Precision Measurement of the Specific Activity of $^{39}$Ar in Atmospheric Argon with the DEAP-3600 Detector Open
The specific activity of the beta decay of $^{39}$Ar in atmospheric argon is measured using the DEAP-3600 detector. DEAP-3600, located 2 km underground at SNOLAB, uses a total of (3269 $\pm$ 24) kg of liquid argon distilled from the atmosp…
View article: The Sum of Its Parts: Visual Part Segmentation for Inertial Parameter Identification of Manipulated Objects
The Sum of Its Parts: Visual Part Segmentation for Inertial Parameter Identification of Manipulated Objects Open
To operate safely and efficiently alongside human workers, collaborative robots (cobots) require the ability to quickly understand the dynamics of manipulated objects. However, traditional methods for estimating the full set of inertial pa…
View article: Remixed Eulerian numbers
Remixed Eulerian numbers Open
Remixed Eulerian numbers are a polynomial q -deformation of Postnikov’s mixed Eulerian numbers. They arose naturally in previous work by the authors concerning the permutahedral variety and subsume well-known families of polynomials such a…
View article: Down-up algebras and chromatic symmetric functions
Down-up algebras and chromatic symmetric functions Open
We establish Guay-Paquet's unpublished linear relation between certain chromatic symmetric functions by relating his algebra on paths to the $q$-Klyachko algebra. The coefficients in this relations are $q$-hit polynomials, and they come up…
View article: Remixed Eulerian numbers
Remixed Eulerian numbers Open
Remixed Eulerian numbers are a polynomial $q$-deformation of Postnikov's mixed Eulerian numbers. They arose naturally in previous work by the authors concerning the permutahedral variety and subsume well-known families of polynomials such …
View article: Local parking procedures on the integers
Local parking procedures on the integers Open
International audience
View article: Learning to Detect Slip with Barometric Tactile Sensors and a Temporal Convolutional Neural Network
Learning to Detect Slip with Barometric Tactile Sensors and a Temporal Convolutional Neural Network Open
The ability to perceive object slip via tactile feedback enables humans to accomplish complex manipulation tasks including maintaining a stable grasp. Despite the utility of tactile information for many applications, tactile sensors have y…
View article: Fast Object Inertial Parameter Identification for Collaborative Robots
Fast Object Inertial Parameter Identification for Collaborative Robots Open
Collaborative robots (cobots) are machines designed to work safely alongside people in human-centric environments. Providing cobots with the ability to quickly infer the inertial parameters of manipulated objects will improve their flexibi…
View article: Learning to Detect Slip with Barometric Tactile Sensors and a Temporal\n Convolutional Neural Network
Learning to Detect Slip with Barometric Tactile Sensors and a Temporal\n Convolutional Neural Network Open
The ability to perceive object slip via tactile feedback enables humans to\naccomplish complex manipulation tasks including maintaining a stable grasp.\nDespite the utility of tactile information for many applications, tactile\nsensors hav…
View article: The Permutahedral Variety, Mixed Eulerian Numbers, and Principal Specializations of Schubert Polynomials
The Permutahedral Variety, Mixed Eulerian Numbers, and Principal Specializations of Schubert Polynomials Open
We compute the expansion of the cohomology class of the permutahedral variety in the basis of Schubert classes. The resulting structure constants $a_w$ are expressed as a sum of normalized mixed Eulerian numbers indexed naturally by reduce…