RTT Agentic Module: Reciprocals of Partition Polynomials

reciprocals-partition-polynomials_module.json — Agentic module schema role assignments

Module ID: reciprocals_partition_polynomials_rtt
Source paper: https://arxiv.org/pdf/2605.21718

This module wraps the paper “Reciprocals of Partition Polynomials” in RTT operator grammar.
It preserves the authors’ mathematics while exposing the structural regimes that govern partition polynomials, their reciprocals, and the associated zero and asymptotic behavior.

1. Purpose#

Make the paper agentic and machine‑navigable.
Clarify the regime structure behind reciprocals of partition polynomials.
Provide students with a clean conceptual map.
Support AI agents in reasoning over the paper without drift.

2. Core RTT view of the paper#

The paper studies:

Partition polynomials (P_n(q)) arising from truncated partition generating functions.
Their reciprocals (1/P_n(q)) as analytic objects.
The zeros of (P_n(q)) and poles of (1/P_n(q)).
The asymptotic behavior of coefficients and values as (n) grows.

The proofs move between combinatorial partition data and complex‑analytic properties of polynomials and their reciprocals.
This module makes those transitions explicit.

3. RTT structures in this module#

Regimes#

partition_polynomial_regime
reciprocal_regime
zero_distribution_regime
asymptotic_regime

Tensions#

finite_vs_infinite_generating
combinatorial_vs_analytic
zeros_vs_coefficients

Transitions#

truncation_to_polynomial_transition
polynomial_to_reciprocal_transition
zeros_to_asymptotics_transition

4. Operators#

partition_polynomial_operator — constructs (P_n(q)).
reciprocal_operator — forms (1/P_n(q)) and tracks poles.
zero_distribution_operator — analyzes zeros/poles.
asymptotic_operator — derives asymptotic estimates.

5. How to use this module#

Students:
Use this README alongside the PDF to see how partition combinatorics and complex analysis interact.
Researchers:
Query the module’s regimes and operators to explore structural dependencies.
Agents:
Treat module.json as the canonical structural map of the paper.

6. Provenance#

Module authoring: TriadicFrameworks (RTT / agentic mapping).
Original content: Authors of arXiv:2605.21718.
License: Open educational use permitted.

`diagram.txt`#

      +------------------------------------------------------+
      | reciprocals_partition_polynomials_rtt                |
      +------------------------------------------------------+
 
REGIMES
  [R1] partition_polynomial_regime
  [R2] reciprocal_regime
  [R3] zero_distribution_regime
  [R4] asymptotic_regime
 
TENSIONS
  [T1] finite_vs_infinite_generating   (R1 <--> R2)
  [T2] combinatorial_vs_analytic       (R1/R2 <--> R3/R4)
  [T3] zeros_vs_coefficients           (R3 <--> R4)
 
TRANSITIONS
  [X1] truncation_to_polynomial_transition
  [X2] polynomial_to_reciprocal_transition
  [X3] zeros_to_asymptotics_transition
 
FLOW
  partition_polynomial_regime (R1)
        |
        v
  reciprocal_regime (R2)
        |
        v
  zero_distribution_regime (R3)
        |
        v
  asymptotic_regime (R4)

Updated Jun 20, 2026