Related papers: Reduced decompositions and commutation classes
We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are…
We consider permutation classes having two basis elements of size three and one further basis element. We completely classify the possible enumeration sequences of such classes and demonstrate that there are far fewer of them than might be…
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases…
The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique- and rank-width of graphs, because it is one of the minimal hereditary classes of…
The properties of the reduced density matrix describing an interval of N sites in an infinite chain of free electrons are investigated. A commuting operator is found for arbitrary filling and also for open chains. For a half filled periodic…
We propose the Relational Tucker3 (RT) decomposition for multi-relational link prediction in knowledge graphs. We show that many existing knowledge graph embedding models are special cases of the RT decomposition with certain predefined…
The higher Bruhat orders $\mathcal{B}(n,k)$ were introduced by Manin-Schechtman to study discriminantal hyperplane arrangements and subsequently studied by Ziegler, who connected $\mathcal{B}(n,k)$ to oriented matroids. In this paper, we…
Given a permutation of size $n$, we consider its associated grid graph whose $i$th column has height equal to the $i$th entry, with vertical edges between consecutive levels and horizontal edges between equal levels in adjacent columns. We…
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…
The classical permutohedron Perm is the convex hull of the points (w(1),...,w(n)) in R^n where w ranges over all permutations in the symmetric group. This polytope has many beautiful properties -- for example it provides a way to visualize…
Let $s$ be West's deterministic stack-sorting map. A well-known result (West) is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations…
In 1965, Steinberg's study of conjugacy classes in connected reductive groups led him to construct an affine subspace parametrising regular conjugacy classes, which he noticed is also a cross section for the conjugation action by the…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
Given a bounded operator $Q$ on a Hilbert space $\mathcal{H}$, a pair of bounded operators $(T_1, T_2)$ on $\mathcal{H}$ is said to be $Q$-commuting if one of the following holds: \[ T_1T_2=QT_2T_1 \text{ or }T_1T_2=T_2QT_1 \text{ or…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.
We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the $n$-th Weyl algebra of differential operators. This approach gives a graph-theoretic combinatorial view of the normal ordering problem…
Many important statistics of signed permutations are realized in the corresponding permutation tableaux or bare tableaux of type $B$: Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…