Related papers: Hall-Littlewood plane partitions and KP

Let $\Lambda$ be the space of symmetric functions and $V_k$ be the subspace spanned by the modified Schur functions $\{S_\lambda[X/(1-t)]\}_{\lambda_1\leq k}$. We introduce a new family of symmetric polynomials,…

We consider KP tau function of hypergeometric type $\tau({\bf t},T,{\bf t}^*)$, where the set ${\bf t}$ is the KP higher times and $T,{\bf t}^*$ are sets of parameters. Fixing ${\bf t}^*$, we find that $\tau({\bf t},T,{\bf t}^*)$ is an…

We study families of partitions with gap conditions that were introduced by Schur and Andrews, and describe their fundamental connections to combinatorial q-series and automorphic forms. In particular, we show that the generating functions…

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack…

The Bernstein operator $\mathbf{B}_n$ acts on a Schur function $S_\lambda$ by appending a part to the index, i.e., $\mathbf{B}_n S_\lambda=S_{(n,\lambda)}$. This provides a method of constructing the vertex operator representation of Schur…

Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and…

We identify the dessin partition function with the partition function of the Laguerre unitary ensemble (LUE). Combined with the result due to Cunden et al on the relationship between the LUE correlators and strictly monotone Hurwitz numbers…

In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., $r$-rowed for $r\geq 2$) tight cylindric partitions, we provide analogs of the Corteel--Welsh functional equations. We prove…

Ramanujan's celebrated congruences of the partition function $p(n)$ have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational polynomial functions yields a general theorem used to…

We derive a factorization theorem that allows for resummation of small-$x$ logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor $W^{\mu\nu}$ in deep…

The ({\em classical}, {\em small quantum}, {\em equivariant}) cohomology ring of the grassmannian $G(k,n)$ is generated by certain derivations operating on an exterior algebra of a free module of rank $n$ ({\em Schubert Calculus on a…

We study plane partitions satisfying condition $a_{n+1,m+1}=0$ (this condition is called "pit") and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane…

$W$-representation realizes partition functions by an action of a cut-and-join-like operator on the vacuum state with a zero-mode background. We provide explicit formulas of this kind for $\beta$- and $q,t$-deformations of the simplest…

We use Bott-Samelson resolutions of Schubert varieties in Grassmannians along with equiariant localization techniques to show that the factorial Schur functions and the factorial Grothendieck polynomials represent Schubert classes in…

We study the row-space partition and the pivot partition on the matrix space $\mathbb{F}_q^{n \times m}$. We show that both these partitions are reflexive and that the row-space partition is self-dual. Moreover, using various combinatorial…

Using the quadratic transformation and the generating function method we Perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We…

The 't~Hooft partition function~$\mathcal{Z}_{\text{tH}}[E;B]$ of an $SU(N)$ gauge theory with the $\mathbb{Z}_N$ 1-form symmetry is defined as the Fourier transform of the partition function~$\mathcal{Z}[B]$ with respect to the…

The $K$-theoretic Schur $P$- and $Q$-functions $GP_\lambda$ and $GQ_\lambda$ may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmetric functions are the shifted analogues of…

We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle…

The generating function of reverse plane partitions of a fixed shape factors into a product featuring the hook-lengths of this shape. This result, which was first obtained by Stanley, can be explained bijectively using the Hillman-Grassl…