arXiv subjects

Teemu Lundström

Publications and source records attributed to Teemu Lundström.

4 recordsLinked to original sources

arXiv2026

Order polytopes of crown posets

In the last decade, the order polytope of the zigzag poset has been thoroughly studied. A related poset, called \emph{crown poset}, obtained by adding an extra cover relation between the endpoints of an even zigzag poset, is not so well understood. In this paper, we study the order polytopes of crown posets. We provide explicit formulas for their $f$-polynomials, and show that the sequence of coefficients of each $f$-polynomial is log-concave and asymptotically normal. We provide recursive formulas for their Ehrhart polynomial, giving a counterpart to formulas found in the zigzag case by Petersen--Zhuang (2025). We use these formulas to simplify a computation by Ferroni--Morales--Panova (2025) of the linear term of the order polynomial of these posets. Furthermore, we provide a combinatorial interpretation for the coefficients of the $h^*$-polynomial in terms of the cyclic swap statistic on cyclically alternating permutations, which provides a circular version of a result by Coons--Sullivant (2023).

math.CO↗

arXiv2026

Two-Dimensional Faces of Order and Chain Polytopes

We give an explicit combinatorial description of the two-dimensional faces of both the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a partially ordered set $P$. Using these descriptions, we show that for any $P$, $\mathcal{C}(P)$ has equally many square faces, and at least as many triangular faces, as $\mathcal{O}(P)$ does. Moreover, the inequality is shown to be strict except when $\mathcal{O}(P)$ and $\mathcal{C}(P)$ are unimodularly equivalent. This proves the case $i=2$ of a conjecture by Hibi and Li.

math.CO↗

arXiv2025

Simplex inequalities of order and chain polytopes of recursively defined posets

In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint unions and ordinal sums, then $\mathcal{C}(P)$ has at least as many $k$-dimensional simplex faces as $\mathcal{O}(P)$ does, for each dimension $k$. This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered.

math.CO↗

arXiv2024

$f$-vector inequalities for order and chain polytopes

The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the $f$-vectors of these polytopes. We investigate how the order and chain polytopes behave under disjoint unions and ordinal sums of posets, and how the $f$-vectors of these polytopes are expressed in terms of $f$-vectors of smaller polytopes. Our focus is on comparing the $f$-vectors of the order and chain polytope built from the same poset. In our main theorem we prove that for a family of posets built inductively by taking disjoint unions and ordinal sums of posets, for any poset $\mathcal{P}$ in this family the $f$-vector of the order polytope of $\mathcal{P}$ is component-wise at most the $f$-vector of the chain polytope of $\mathcal{P}$.

math.CO↗