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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20010 |
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| _version_ | 1866917736318238720 |
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| author | Ji, Ce Tang, Qian Yang, Chenglang |
| author_facet | Ji, Ce Tang, Qian Yang, Chenglang |
| contents | We study some kinds of generalizations of Schröder paths below a line with rational slope and derive the $q$-difference equations that are satisfied by their generating functions. As a result, we establish a relation between the generating function of generalized Schröder paths with backwards and the wave function corresponding to colored HOMFLY-PT polynomials of torus knot $T_{1,f}$. We also give a combinatorial proof of a recent result by Stošić and Sułkowski, in which the standard generalized Schröder paths are related to the superpolynomial of reduced colored HOMFLY-PT homology of $T_{1,f}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schröder Paths, Their Generalizations and Knot Invariants Ji, Ce Tang, Qian Yang, Chenglang Combinatorics Mathematical Physics We study some kinds of generalizations of Schröder paths below a line with rational slope and derive the $q$-difference equations that are satisfied by their generating functions. As a result, we establish a relation between the generating function of generalized Schröder paths with backwards and the wave function corresponding to colored HOMFLY-PT polynomials of torus knot $T_{1,f}$. We also give a combinatorial proof of a recent result by Stošić and Sułkowski, in which the standard generalized Schröder paths are related to the superpolynomial of reduced colored HOMFLY-PT homology of $T_{1,f}$. |
| title | Schröder Paths, Their Generalizations and Knot Invariants |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2407.20010 |