Institution profile

University of Winnipeg

Academic institutionnorthamerica · ca
Official website
Research library4linked papers
Opportunities0open roles
Selected work

Representative Papers

An example of an automatic sequence with non-regular abelian complexity

Oct 02, 2026

This work addresses the open problem posed by Madill and Rampersad concerning the Abelian complexity of automatic sequences. By integrating techniques from formal language theory and combinatorics, the study investigates the structural properties and complexity measures of automatic sequences. The primary contribution is the construction of a 2-automatic sequence whose Abelian complexity is rigorously proven not to be 2-regular. This counterexample refutes the prevailing theoretical assumption that the Abelian complexity of automatic sequences is necessarily regular, thereby filling a significant gap in the existing literature. Ultimately, these findings provide essential theoretical foundations and offer new perspectives for future research on the complexity of automatic sequences.

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Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing

Jul 10, 2026

This study addresses the challenge of dynamic food pricing, which can enhance retailer profits but often raises consumer fairness concerns due to inadequate integration of sales forecasting and price equity in existing approaches. The authors propose a novel framework that uniquely embeds consumer price index (CPI)-based fairness constraints directly into the sales prediction model. Leveraging a log-log ARDL specification to estimate price elasticity, the framework combines linear programming with simulated annealing to solve both single-item and multi-item pricing problems. Empirical results demonstrate that unconstrained optimization frequently drives prices to their upper bounds, whereas CPI-anchored pricing yields more conservative solutions that balance sales objectives with consumer affordability. Furthermore, CPI deflation reveals that apparent positive nominal elasticities are largely driven by inflation effects, underscoring the transparency and enhanced fairness perception of the proposed mechanism.

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Words with factor somplexity $2n+1$ and minimal critical exponent

Jul 12, 2025

This paper addresses the minimal critical exponent problem for infinite words with factor complexity exactly $2n+1$, aiming to verify the conjecture of Shallit and Shur that the critical exponent admits a lower bound $mu = 2 + 1/(lambda^2 - 1)$, where $lambda approx 1.75488$ is the unique real root of $x^3 - 2x^2 + x - 1 = 0$. Using algebraic combinatorics and spectral methods—leveraging analytic properties of polynomial roots—we establish, for the first time, a rigorous proof that every infinite word with factor complexity $2n+1$ has critical exponent at least $mu approx 2.4808726$. This bound is tight and theoretically optimal. The result confirms a long-standing open conjecture and provides a fundamental case study on the interplay between factor complexity and repetition in combinatorics on words. Moreover, it advances the structural understanding of automatic sequences and irrational rotation sequences.

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Recent publications

Latest Papers

An example of an automatic sequence with non-regular abelian complexity

Oct 02, 2026

This work addresses the open problem posed by Madill and Rampersad concerning the Abelian complexity of automatic sequences. By integrating techniques from formal language theory and combinatorics, the study investigates the structural properties and complexity measures of automatic sequences. The primary contribution is the construction of a 2-automatic sequence whose Abelian complexity is rigorously proven not to be 2-regular. This counterexample refutes the prevailing theoretical assumption that the Abelian complexity of automatic sequences is necessarily regular, thereby filling a significant gap in the existing literature. Ultimately, these findings provide essential theoretical foundations and offer new perspectives for future research on the complexity of automatic sequences.

0 citationsRead paper

Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing

Jul 10, 2026

This study addresses the challenge of dynamic food pricing, which can enhance retailer profits but often raises consumer fairness concerns due to inadequate integration of sales forecasting and price equity in existing approaches. The authors propose a novel framework that uniquely embeds consumer price index (CPI)-based fairness constraints directly into the sales prediction model. Leveraging a log-log ARDL specification to estimate price elasticity, the framework combines linear programming with simulated annealing to solve both single-item and multi-item pricing problems. Empirical results demonstrate that unconstrained optimization frequently drives prices to their upper bounds, whereas CPI-anchored pricing yields more conservative solutions that balance sales objectives with consumer affordability. Furthermore, CPI deflation reveals that apparent positive nominal elasticities are largely driven by inflation effects, underscoring the transparency and enhanced fairness perception of the proposed mechanism.

0 citationsRead paper

Words with factor somplexity $2n+1$ and minimal critical exponent

Jul 12, 2025

This paper addresses the minimal critical exponent problem for infinite words with factor complexity exactly $2n+1$, aiming to verify the conjecture of Shallit and Shur that the critical exponent admits a lower bound $mu = 2 + 1/(lambda^2 - 1)$, where $lambda approx 1.75488$ is the unique real root of $x^3 - 2x^2 + x - 1 = 0$. Using algebraic combinatorics and spectral methods—leveraging analytic properties of polynomial roots—we establish, for the first time, a rigorous proof that every infinite word with factor complexity $2n+1$ has critical exponent at least $mu approx 2.4808726$. This bound is tight and theoretically optimal. The result confirms a long-standing open conjecture and provides a fundamental case study on the interplay between factor complexity and repetition in combinatorics on words. Moreover, it advances the structural understanding of automatic sequences and irrational rotation sequences.

0 citationsRead paper