Published August 11, 2026 | Version v2
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Construction, Functionalization, and Truncation Phenomena in Higher-Order q Analog Accumulation Matrices

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Description

We present a systematic construction of higher-order q-analog accumulation matrices that unify
combinatorial growth (skeleton) with exponential growth (power expansion). By introducing
binomial coefficients as variable bases and implementing a three-layer operator composition—
skeleton generation, power expansion, and cumulative summation—we construct complete
matrices for orders d = 3 through d = 6. A key finding is the exponential truncation phenomenon
observed in the low-order regime (d = 3), where order constraints induce exponent degeneration
at specific matrix entries, a behavior absent in higher orders (d ≥ 4). Through forward difference
operator verification, we establish that these matrices preserve the fundamental discrete calculus
property of mutual inversion between summation and differencing. This work extends classical
Q₁-analog theory to higher-order discrete systems and provides a novel algebraic framework for
modeling coupled combinatorial-exponential growth phenomena.

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Construction, Functionalization, and Truncation Phenomena in Higher-Order q-Analog Accumulation Matrices.pdf

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Additional details

Related works

Is supplement to
Dataset: q-analog (Other)

Dates

Accepted
2026-05-19

References

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