相关论文: BPS state counting on singular varieties

In this letter we calculate the exact partition function for free bosons on the plane with lacunae. First the partition function for a plane with two spherical holes is calculated by matching exactly for the infinite set of Wilson…

We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…

The paper introduce a new type of partitions where the largest part appears exactly once, and the remaining parts constitute a partition of that largest part. We derive the generating function associated with these partitions and…

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…

MacMahon showed that the generating function for partitions into at most $k$ parts can be decomposed into a partial fractions-type sum indexed by the partitions of $k$. In this present work, a generalization of MacMahon's result is given,…

In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of $1$'s in the partitions of $n$. A new expansion for Euler's partition function $p(n)$ is derived in this…

Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are…

We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of…

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance…

We construct a statistical model that correctly reproduces the BPS partition function of D4-D2-D0 bound states on the resolved conifold. We prove that the known partition function of the BPS indices is reproduced by the counting "triangular…

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good…

We review some simple group theoretical properties of BPS states, in relation with the singular homology of level surfaces. Primary focus is on classical and quantum N=2 supersymmetric Yang-Mills theory, though the considerations can be…

BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper…

We present recent results in semileptonic and non-leptonic exclusive $B_c$ decays to charmonium states both in $S$-wave, $J/\psi$ and $\eta_c$, and in $P$-wave, $\chi_{cJ}$ and $h_c$. The analysis, based on the heavy quark spin symmetry…

We reformulate the lifting problem in the D1-D5 CFT as a supercharge cohomology problem, and enumerate BPS states according to the fortuitous/monotone classification. Working in the deformed $T^4$ symmetric orbifold theory, we give precise…

We give a construction of general holomorphic quarter BPS operators in $ \mathcal{N}=4$ SYM at weak coupling with $U(N)$ gauge group at finite $N$. The construction employs the M\"obius inversion formula for set partitions, applied to…

Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of…

Extensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these…