相关论文: Enumeration of bilaterally symmetric 3-noncrossing…

We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of distinguished subwords. Second, we give a type-uniform proof…

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of…

Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…

One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…

We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of…

We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…

Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for…

Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…

Set partitions are arrangements of distinct objects into groups. The problem of listing all set partitions arises in a variety of settings, in particular in combinatorial optimization tasks. After a brief review, we give practical…

We propose a formula for the enumeration of closed lattice random walks of length $n$ enclosing a given algebraic area. The information is contained in the Kreft coefficients which encode, in the commensurate case, the Hofstadter secular…

There are two natural simplicial complexes associated to the noncrossing partition lattice: the order complex of the full lattice and the order complex of the lattice with its bounding elements removed. The latter is a complex that we call…

A \emph{set partition} of the set $[n]=\{1,...c,n\}$ is a collection of disjoint blocks $B_1,B_2,...c, B_d$ whose union is $[n]$. We choose the ordering of the blocks so that they satisfy $\min B_1<\min B_2<...b<\min B_d$. We represent such…

Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain…

Consideration of a classification of the number of partitions of a natural number according to the members of sub-partitions differing from unity leads to a non-recursive formula for the number of irreducible representations of the…

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…

We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional…

An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed…

Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a…

We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model…

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…