Related papers: Permutation totally symmetric self-complementary p…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for…
Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…
In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain…
The derangement polynomial for the symmetric group enumerates derangements by the number of excedances. It can be interpreted as the local $h$-polynomial, in the sense of Stanley, of the barycentric subdivision of the simplex. Motivated by…
Alternating sign trapezoids have recently been introduced as a generalisation of alternating sign triangles. Fischer established a threefold refined enumeration of alternating sign trapezoids and provided three statistics on column strict…
The stack sort algorithm has been the subject of extensive study over the years. In this paper we explore a generalized version of this algorithm where instead of avoiding a single decrease, the stack avoids a set $T$ of permutations. We…
We derive a simple bijection between geometric plane perfect matchings on $2n$ points in convex position and triangulations on $n+2$ points in convex position. We then extend this bijection to monochromatic plane perfect matchings on…
We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never…
Recall that an excedance of a permutation $\pi$ is any position $i$ such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it…
Let $e^{2\pi i\Q}$ denote the set of roots of unity. We consider subsets $E\subset e^{2\pi i\Q}$ that are quasi-independent or algebraically independent (as subsets of the discrete plane). A bijective map on $e^{2\pi i\Q}$ preserves the…
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
We consider the problem of finding a bijection between the sets of alternating sign matrices and of totally symmetric self complementary plane partitions, which can be reformulated using Gog and Magog triangles. In a previous work we…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
We introduce a new basis of the Temperley-Lieb algebra. It is defined using a bijection between noncrossing partitions and fully commutative elements together with a basis introduced by Zinno, which is obtained by mapping the simple…
We introduce a novel combinatorial structure called pointed building sets, which can be viewed as families of lattices equipped with compatibility relations. To each pointed building set $\mathsf{B}$, we associate a complete lattice…
The perfect matching association scheme is a set of relations on the perfect matchings of the complete graph on $2n$ vertices. The relations between perfect matchings are defined by the cycle structure of the union of any two perfect…
Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…
The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix…
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs,…