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Congruence for Lattice Path Models with Filter Restrictions and Long Steps

Author

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  • Dmitry Solovyev

    (Euler International Mathematical Institute, Pesochnaya nab. 10, 197022 St. Petersburg, Russia
    Yau Mathematical Sciences Center, Tsinghua University, Jingzhai, Beijing 100084, China
    Department of Quantum Mechanics, Saint Petersburg State University, 7-9 Universitetskaya Emb., 199034 St. Petersburg, Russia)

Abstract

We derive a path counting formula for a two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves the problem of finding an explicit formula for multiplicities of modules in tensor product decomposition of T ( 1 ) ⊗ N for U q ( s l 2 ) with divided powers, where q is a root of unity. Combinatorial treatment of this problem calls for the definition of congruence of regions in lattice path models, properties of which are explored in this paper.

Suggested Citation

  • Dmitry Solovyev, 2022. "Congruence for Lattice Path Models with Filter Restrictions and Long Steps," Mathematics, MDPI, vol. 10(22), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4209-:d:969561
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    Cited by:

    1. Irina Cristea & Hashem Bordbar, 2023. "Preface to the Special Issue “Algebraic Structures and Graph Theory”," Mathematics, MDPI, vol. 11(15), pages 1-4, July.

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