Related papers: Promotion permutations for tableaux
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator…
We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees and binary sequences. On the combinatorial side, we study the rotation lattices on permutrees and their lattice homomorphisms, unifying the weak order,…
We introduce the notion of "type" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…
Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for…
If one attaches shifted copies of a skew tableau to the right of itself and rectifies, at a certain point the copies no longer experience vertical slides, a phenomenon called tableau stabilization. While tableau stabilization was originally…
We show that the transition matrix from the polytabloid basis to the web basis of the irreducible $\mathfrak{S}_{2n}$-representation of shape $(n,n)$ has nonnegative integer entries. This proves a conjecture of Russell and Tymoczko.
In this work we study Sch\"utzenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as $m-$diagrams. In particular, we prove that certain internal structures of SYT are preserved under…
This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…
This work represents an in-depth study of the structural behavior of the Collatz sequences. We consider a finite arithmetic progression with a common difference is 2 and the number of terms in the sequence is equal to 2^n . After, we…
We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a $n$-round Prisoner's…
Variational inference algorithms such as belief propagation have had tremendous impact on our ability to learn and use graphical models, and give many insights for developing or understanding exact and approximate inference. However,…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
We give another bijective proof of a result of Corteel and Nadeau. We find a generating function related to unrestricted columns of permutation tableaux. As a consequence, we obtain a sign-imbalance formula for permutation tableaux. We…
The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together…
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers…
Recommender systems play a fundamental role in web applications in filtering massive information and matching user interests. While many efforts have been devoted to developing more effective models in various scenarios, the exploration on…