Related papers: Stack-sorting simplices: geometry and lattice-poin…

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…

To classify the lattice polytopes with a given $\delta$-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular,…

We introduce Lipschitz functions on a finite partially ordered set $P$ and study the associated Lipschitz polytope $L(P)$. The geometry of $L(P)$ can be described in terms of descent-compatible permutations and permutation statistics that…

The Birkhoff polytope $B_n$ is the convex hull of all $n\times n$ permutation matrices in $\mathbb{R}^{n\times n}$. We compute the combinatorial symmetry group of the Birkhoff polytope. A representation polytope is the convex hull of some…

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…

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the…

In this paper we study partitions whose successive ranks belong to a given set. We enumerate such partitions while keeping track of the number of parts, the largest part, the side of the Durfee square, and the height of the Durfee…

If $P$ is a lattice polytope (that is, the convex hull of a finite set of lattice points in $\mathbf{R}^n$), then every sum of $h$ lattice points in $P$ is a lattice point in the $h$-fold sumset $hP$. However, a lattice point in the…

Let $\mathcal D_n$ denote the average number of iterations of West's stack-sorting map $s$ that are needed to sort a permutation in $S_n$ into the identity permutation $123\cdots n$. We prove that…

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…

The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several different formulas for these polynomials. We also study a more…

For any finite connected poset $P$, Galashin introduced a simple convex $(|P|-2)$-dimensional polytope $\mathscr{A}(P)$ called the poset associahedron. For a certain family of posets, whose poset associahedra interpolate between the…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$,…

We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and…

Hibi, Yoshida, and the author classified Gorenstein simplices which are not lattice pyramids and whose \(h^*\)-polynomials are of the form \(1+t^k+t^{2k}+\cdots+t^{(v-1)k}\) when \(v\) is a prime number or the product of two prime numbers.…

We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving…

Considering $n\times n\times n$ stochastic tensors $(a_{ijk})$ (i.e., nonnegative hypermatrices in which every sum over one index $i$, $j$, or $k$, is 1), we study the polytope ($\Omega_{n}$) of all these tensors, the convex set ($L_n$) of…

In this paper we examine the sorting operator $T(LnR)=T(R)T(L)n$. Applying this operator to a permutation is equivalent to passing the permutation reversed through a stack. We prove theorems that characterise $t$-revstack sortability in…

We study a sorting machine consisting of two stacks in series where the first stack has the added restriction such that entries in the stack must be in decreasing order from top to bottom. We give the basis of the class of permutations that…