相关论文: Combinatorial Wall-Crossing and the Mullineux Invo…

We introduce a statistic $\pmaj$ on partitions of $[n]=\{1,2,..., n\}$, and show that it is equidistributed with the number of 2-crossings over partitions of $[n]$ with given sets of minimal block elements and maximal block elements. This…

A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a…

Recent quantum reconstruction projects demand pure unitary time evolution which seems to contradict the collapse postulate. Inspired by Zurek's environment assisted invariance idea, a natural unitary realization of wavefunction collapse is…

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten invariants on geometric invariant theory (git) quotients related by a change in polarization. The wall-crossing terms are gauged Gromov-Witten invariants…

In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of…

We show how certain suitably modified N-modular diagrams of integer partitions provide a nice combinatorial interpretation for the general term of Zeilberger's KOH identity. This identity is the reformulation of O'Hara's famous proof of the…

In a 1976 landmark paper, Gordon James defined the regularisation maps on integer partition, yielding certain decomposition numbers for modular representations of $\mathfrak{S}_n$. We describe a generalisation of James's regularisation map…

In this paper, we apply the combinatorial proof technique of Description, Involution, Exceptions (DIE) to prove various known identities for the joint cumulant. Consider a set of random variables $S = \{X_1,..., X_n\} $. Motivated by the…

We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has…

Coalescing particles on a line merge when they meet. As they do, their basins of attraction merge and the walls between basins disappear. If every site is initially occupied, these walls at any positive time form a Pfaffian point process:…

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a…

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…

Combinatorial transition matrices arise frequently in the theory of symmetric functions and their generalizations. The entries of such matrices often count signed, weighted combinatorial structures such as semistandard tableaux, rim-hook…

We show that the wall crossing bijections between simples of the category O of the rational Cherednik algebras reduce to particular crystal isomorphisms which can be computed by a simple combinatorial procedure on multipartitions of fixed…

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…

We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known…

In this paper, cylindric partitions into profiles $c=(1,1)$ and $c=(2,0)$ are considered. The generating functions into unrestricted cylindric partitions and cylindric partitions into distinct parts with these profiles are constructed. The…

Recently, Babson and Steingrimsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider pattern avoidance for such patterns, and…

One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings--the Penrose, octagonal, and pinwheel tilings are famous examples. We present a…

For a fixed integer $k$, we consider the set of noncrossing partitions, where both the block sizes and the difference between adjacent elements in a block is $1\bmod k$. We show that these $k$-indivisible noncrossing partitions can be…