Related papers: Rowmotion and Echelonmotion

The variety of complete quadrics is the wonderful compactification of $GL_n/O_n$ and admits a cell decomposition into Borel orbits indexed by combinatorial objects called $\mu$-involutions. We study Coxeter-theoretic properties of…

We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results regarding symmetric chain decompositions of the Young posets…

Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $\Upsilon(P)$ and discuss some of the properties of the map $\Upsilon$. In particular, if we regard $\Upsilon(P)$ as a…

Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining…

We prove that if a Bessel sequence in a Hilbert space, that is indexed by a countably infinite group in an invariant manner, can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen…

The classical 1991 result by Brightwell and Winkler states that the number of linear extensions of a poset is #P-complete. We extend this result to posets with certain restrictions. First, we prove that the number of linear extension for…

Let p be an odd prime number, E an elliptic curve over a number field k, and F/k a Galois extension of degree twice a power of p. We study the Z_p-corank rk_p(E/F) of the p-power Selmer group of E over F. We obtain lower bounds for…

We provide an analysis of the x-dependence of the bare unpolarized, helicity and transversity iso-vector parton distribution functions (PDFs) from lattice calculations employing (maximally) twisted mass fermions. The x-dependence of the…

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum…

In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the…

We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for…

The rowmotion operator acting on the set of order ideals of a finite poset has been the focus of a significant amount of recent research. One of the major goals has been to exhibit homomesies: statistics that have the same average along…

Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…

This paper is centered on covariant dynamics on unimodular random graphs and random networks, namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as…

For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation…

Let $G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy-to-describe bijections $g_{\sigma,\sigma^*}$ between spanning trees of $G$ and $(\sigma,\sigma^*)$-compatible orientations, where…

Incoherent exciton dynamics in one-dimensional perfect lattices with traps at sites arranged according to aperiodic deterministic sequences is studied. We focus our attention on Thue-Morse and Fibonacci systems as canonical examples of…

We introduce two partially ordered sets, $P^A_n$ and $P^B_n$, of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of $P^A_n$ and $P^B_n$ are subsets of the symmetric and the hyperoctahedral…

We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e. without appealing to the classification…