Related papers: BKP plane partitions
In this article, we study the arithmetic properties of the partition function $p_8(n)$, the number of 8-colour partitions of $n$. We prove several Ramanujan type congruences modulo higher powers of 2 for the function $p_8(n)$ by finding…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
We calculate the parton level cross section for the production of two jets that are far apart in rapidity, subject to a limitation on the total transverse momentum Q_0 in the interjet region. We specifically address the question of how to…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
In this work, we investigate the arithmetic properties of $p_{1,7^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $7^k$. By constructing generating functions for…
Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…
MacMahon's classical theorem on the number of boxed plane partitions has been generalized in several directions. One way to generalize the theorem is to view boxed plane partitions as lozenge tilings of a hexagonal region and then…
We compute exact finite-rank BPS generating functions for the fermionic matrix model with single-trace supercharge $Q_p=\operatorname{tr}(\Psi^p)$ at $(p,N)=(5,3),(5,4),(5,5),(7,4)$, together with partial data at $(7,5)$. In all complete…
Probabilities of photon counts at the output of a multiport optical device are generalised for optical sources of arbitrary quantum states in partially distinguishable optical modes. For the single-mode photon sources, the generating…
We propose a new baryogenesis scenario based on coherent production and mixing of different fermionic species. The mechanism is operative during phase transitions, at which the fermions acquire masses via Yukawa couplings to scalar fields.…
We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…
A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. We consider Balanced Connected…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
We generalize the generating formula for plane partitions known as MacMahon's formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald's symmetric functions. The…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
We report on a work in progress, whose goal is a systematic field theoretical derivation of the quantum transport equations for baryon production in the electroweak plasma at a first order phase transition in the limit of slowly varying…
We prove a pair of (mod 10) partition identities. The sum sides involve three-colored partitions into distinct parts, while the product sides are the generating functions for distinct partitions times the Rogers-Ramanujan products. Our…
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The…
\noindent The simultaneous partition problems are classical problems of the combinatorial geometry which have the natural flavor of the equivariant topology. The $k$-fan partition problems have attracted a lot of attention \cite{Aki2000},…
We define new partition functions for theories with targets on toric singularities via products of old partition functions on crepant resolutions. We compute explicit examples and show that the new partition functions turn out to be…