# An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes

## TL;DR

This paper introduces an efficient data structure that leverages compressed ideal lattice representations to count linear extensions, compute jump numbers, and facilitate distributed computation in posets.

## Contribution

It presents a novel data structure and approach for efficiently processing poset ideals, enabling scalable distributed computations for related combinatorial problems.

## Key findings

- Efficient counting of linear extensions achieved.
- Compressed ideal lattice representation reduces computational complexity.
- Supports distributed computation for large posets.

## Abstract

Achieving the goals in the title (and others) relies on a cardinality-wise scanning of the ideals of the poset. Specifically, the relevant numbers attached to the k+1 element ideals are inferred from the corresponding numbers of the k-element (order) ideals. Crucial in all of this is a compressed representation (using wildcards) of the ideal lattice. The whole scheme invites distributed computation.