Related papers: On equidistribution theorem for plane partitions
Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.
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…
We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental…
We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…
We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by -1 as proposed by…
Schutzenberger's theorem for the ordinary RSK correspondence naturally extends to Chen et. al's correspondence for matchings and partitions. Thus the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an…
In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…
Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…
This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting of the…
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in $[0, 1]^d$. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and…
We give a direct deduction and proof of two identities in the theory of plane partitions. The first one is known to enumerate the traces of plane partitions. The second one comes without any combinatorial interpretation.
We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…
Some conjectures on partition hook lengths, recently stated by the author, have been proved and generalized by Stanley, who also needed a formula by Andrews, Goulden and Jackson on symmetric functions to complete his derivation. Another…
We study the asymptotic behaviour of the trace (the sum of the diagonal parts) of a plane partition of the positive integer n, assuming that this parfition is chosen uniformly at random from the set of all such partitions.
We show that L\"uck's conjecture on torsion growth in homology implies that two 3-manifolds have equal volume if the fundamental groups have the same set of finite quotients.
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by…
A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective…
Major Percy A. MacMahon's first paper on plane partitions included a conjectured generating function for symmetric plane partitions. This conjecture was proven almost simultaneously by George Andrews and Ian Macdonald, Andrews using the…
In this paper, we consider plane partitions $\text{PP}(\lambda; m)$ of a given shape $\lambda$, with entries at most $m$. We prove that the distributions of two statistics on $\text{PP}(\lambda; m)$ coincide: one is the number of rows…
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to…