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arXiv · 2605.02786

Double twist knots and lattice paths

Aditya Dwivedi·Ramadevi Pichai
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Abstract

In this work, we explore the combinatorics arising from the quiver generating series of the unreduced $r$-colored HOMFLY-PT polynomial $\bar{P}_r(a,q)$ for some twist-knots and double twist knots. By taking the limit $a = 0$ and $q = 1$, we indeed obtain lattice path models for these knots.

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Aditya Dwivedi, Ramadevi Pichai. 2026-05-04. Double twist knots and lattice paths. https://arxiv.org/abs/2605.02786

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