Inspired by Armin Straub's conjecture () about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, symbolic-computational algorithms, based on non-linear functional recurrences, to generate the generating functions, according to size, ...
For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence that X_s is asymptotically normal...
It lacks a strong implication of the method of division, focusing primarily on the resulting outcome – the existence of distinct parts. However, when the act of dividing implies creating distinct and often equal portions, partition becomes a more appropriate term. Think of the ...
In this second paper under the same title, some more weighted representations are obtained for various classical partition functions including p(n), the number of unrestricted partitions ofn , Q(n), the number of partitions ofn into distinct parts and the Rogers-Ramanujan partitions ofn (of both...
verb (used with object) to divide into parts, sections, or portions: In Western culture, our lives tend to be partitioned into distinct domains, making it almost impossible to view life as a whole. Synonyms:apportion,portion Antonyms:unite ...
Used for creating distinct rooms or areas with more defined separation. 14 Compare with Definitions Divider A movable object that separates parts of a room for organizational purposes. We used a folding screen as a divider to create a study area. 8 Partition Separate or apportion into sections;...
nounThat which divides or separates; that by which different things, or distinct parts of the same thing, are separated; separating boundary; dividing line or space; specifically, an interior wall dividing one part or apartment of a house, a compartment of a room, an inclosure, or the like...
Let $\mathrm{pod}_{-4}(n)$ denote the number of partition quadruples of $n$ where the odd parts in each partition are distinct. We find many arithmetic properties of $\mathrm{pod}_{-4}(n)$ involving the following infinite family of congruences: for any i
partitioning a computer or the web refers to dividing up a single physical hard disk into multiple, separate parts. in terms of computers, these partitions are seen as distinct, independent drives that can each be used to store files and programs. on the internet, partitioning divides a web...
In any 2K2-partition for G, either (i) x,y,x′,y′ are in four distinct parts or (ii) x,x′ are in the same part, say A, and y,y′ are in the same part, say C. The test for a partition of type (i) can be achieved by reduction to a single instance of 2-...