Related papers: Catalan lattices on series parallel interval order…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
The article deals with a lexicographic order in various sequences. Consider the axiomatic of lexicographic series, based on the properties of the natural numbers. Elements of the set are ordered first the code length; further in each sign…
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and we show directly multidimensional…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
We prove a conjecture of Thomas Lam that the face posets of stratified spaces of planar resistor networks are shellable. These posets are called uncrossing partial orders. This shellability result combines with Lam's previous result that…
We introduce two new partial orders on the standard Young tableaux of a given partition shape, in analogy with the strong and weak Bruhat orders on permutations. Both posets are ranked by the major index statistic offset by a fixed shift.…
In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…
We extended the definition of regular dilation to graph products of $\mathbb{N}$, which is an important class of quasi-lattice ordered semigroups. Two important results in dilation theory are unified under our result: namely, Brehmer's…
We introduce a transformation of finite integer sequences, show that every sequence eventually stabilizes under this transformation and that the number of fixed points is counted by the Catalan numbers. The sequences that are fixed are…
We study the error of the number of unimodular lattice points that fall into a dilated and translated parallelogram. By using an article from Skriganov, we see that this error can be compared to an ergodic sum that involves the discrete…
We construct a family of integrable Hamiltonian systems generalizing the relativistic periodic Toda lattice, which is recovered as a special case. The phase spaces of these systems are double Bruhat cells corresponding to pairs of Coxeter…
A barcode is a finite multiset of intervals on the real line. Jaramillo-Rodriguez (2023) previously defined a map from the space of barcodes with a fixed number of bars to a set of multipermutations, which presented new combinatorial…
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 analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition lattice, proving sharp uniform representation stability bounds…
We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices.…
Dyck paths are among the most heavily studied Catalan families. We work with peaks and valleys to uniquely decompose Dyck paths into the simplest objects - prime fragments with a single peak. Each Dyck path is uniquely characterized by a…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the…