Q-polynomial invariant of rooted trees

TL;DR

This paper introduces a new polynomial invariant for rooted trees, highlighting its mathematical interest and potential connections to knot theory, homological algebra, and various scientific disciplines.

Contribution

It presents an elementary, novel polynomial invariant for rooted trees, encouraging further exploration and interdisciplinary connections.

Findings

Proposes a new polynomial invariant for rooted trees.

Connects the invariant to knot theory and homological algebra.

Encourages development of new results and interdisciplinary research.

Abstract

We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, and after reading this essay readers can take part in developing the topic, inventing new results and connections to other disciplines of mathematics, and likely, statistical mechanics, and combinatorial biology. We also provide a (free) translation of the paper in Polish.