Related papers: Labelled well-quasi-order in juxtapositions of per…
We introduce vincular pattern posets, then we consider in particular the quasi-consecutive pattern poset, which is defined by declaring $\sigma \leq \tau$ whenever the permutation $\tau$ contains an occurrence of the permutation $\sigma$ in…
In this paper we give a bijection between the class of permutations that can be drawn on an X-shape and a certain set of permutations that appears in [Knuth] in connection to sorting algorithms. A natural generalization of this set leads us…
An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…
In this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomorphic image ordering (in both its standard and strong forms).…
We study the well-quasi-order (wqo) consisting of the set of finite trees with leaf labels coming from an arbitrary wqo $Q$, ordered by tree homomorphisms which respect the order on the labels. This is a variant of the usual Kruskal tree…
Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…
In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…
We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then generalise the notion of $\sigma$-scattered to partial orders, and use our method…
Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its…
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…
We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A ``pattern'' in a permutation $\sigma$ is the order type of the restriction of $\sigma : [n] \to [n]$ to a subset $S…
A partial automorphism of a semigroup $S$ is any isomorphism between its subsemigroups, and the set all partial automorphisms of $S$ with respect to composition is the inverse monoid called the partial automorphism monoid of $S$. Two…
We introduce a new algebraic concept of an algebra which is "almost" commutative (more precisely "quasi-commutative differential graded algebra" or ADGQ, in French). We associate to any simplicial set X an ADGQ - called D(X) - and show how…
For a hereditary permutation class $\mathcal{C}$, we say that two permutations $\pi$ and $\sigma$ of $\mathcal{C}$ are Wilf-equivalent in $\mathcal{C}$, if $\mathcal{C}$ has the same number of permutations avoiding $\pi$ as those avoiding…
A family of permutations A \subset S_n is said to be intersecting if any two permutations in A agree at some point, i.e. for any \sigma, \pi \in A, there is some i such that \sigma(i)=\pi(i). Deza and Frankl showed that for such a family,…
A permutation is centrosymmetric if it is fixed by a half-turn rotation of its diagram. Initially motivated by a question by Alexander Woo, we investigate the question of whether the growth rate of a permutation class equals the growth rate…
We develop a framework relating semiorthogonal decompositions of a triangulated category $\mathcal{C}$ to paths in its space of stability conditions. We prove that when $\mathcal{C}$ is the homotopy category of a smooth and proper…
We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to $k$-tuples of almost commuting permutations,…
We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle…