In this paper, we compute partitions of the tetrahedron for up to the fourth-order spectral volume reconstruction. Certain optimization is made to these partitions and previously obtained partitions of lower dimensional simplex. These optimized partitions have the smallest Lebesgue constants among currently known spectral volume partitions. Institute for Mathematics and its Applications, Univer...

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

We investigate properties of attainable partitions integers, where a partition $$(n_1,n_2, \dots , n_r)$$ n is if $$\sum (3-2i)n_i\ge 0$$ . Conjecturally, under an extension the Cohen and Lenstra heuristics by Holmin et. al., these correspond to abelian p-groups that appear as class groups imaginary quadratic number fields for infinitely many odd primes p. demonstrate connection integers into t...

Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative numbers. Partitions are then tabulated into lattices and some properties of these lattices are studied. There appears a new identity counting isoscele Ferrers ...

In this note I prove a~claim on determinants of some special tridiagonal matrices. Together with my result about Fibonacci partitions (arXiv:math/0307150), claim allows one to (slightly strengthened) Shallit's such partitions.

A partition of an integer n is graphical if it is the degree sequence of a simple undirected graph It is an open question whether the fraction of partitions of n which are graphical approaches as n approaches in nity A partition is basic if the number of dots in its Ferrers graph is minimum among all partitions with the same rank vector as In this paper we investigate graphical partitions via b...

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are slightly superlinear: the complexity is O(n(lnn)3) in approximate-size sampling and O(n4/3) in exact-size sampling (under a real-arithmetic computation mode...

The comparison of partitions is a central topic in clustering, as well for comparing partitioning algorithms as for classifying nominal variables. In this paper, we deal with the transfer distance between partitions, defined as the minimum number of transfers of one element from its class to another (eventually empty) necessary to turn one partition into the other one. We study the distribution...

We use intermediate symplectic characters to give a proof and variations of Hopkins' conjecture, now proved by Hopkins Lai, on the number shifted plane partitions double staircase shape with bounded entries. In fact, we prove some character identities involving characters, find generating functions for such partitions. The key ingredients are bialternant formula which interpolates between those...