<abstract xmlns="http://www.w3.org/1999/xhtml">

Deodhar [<italic>Geom. Dedicata</italic> 36, no. 1 (1990)] introduced the <italic>defect</italic> statistic on subexpressions of reduced expressions in the symmetric group 𝔖<italic>n</italic> to construct an algorithmic description of the Kazhdan–Lusztig basis of the Hecke algebra <italic>H</italic><italic>n</italic>(<italic>q</italic>). This led Billey–Warrington [<italic>J. Algebraic Combin.</italic> 13, no. 2 (2001)] and the second author [<italic>J. Pure Appl. Algebra</italic> 212 (2008)] to state very explicit combinatorial descriptions of the basis elements indexed by permutations avoiding certain patterns. We extend the above work by producing an exhaustive list of graphical representations of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations <italic>w</italic> ∈𝔖5, 𝔖6.
</abstract>

Deodhar [Geom. Dedicata 36, no. 1 (1990)] introduced the defect statistic on subexpressions of reduced expressions in the symmetric group 𝔖n to construct an algorithmic description of the Kazhdan–Lusztig basis of the Hecke algebra Hn(q). This led Billey–Warrington [J. Algebraic Combin. 13, no. 2 (2001)] and the second author [J. Pure Appl. Algebra 212 (2008)] to state very explicit combinatorial descriptions of the basis elements indexed by permutations avoiding certain patterns. We extend the above work by producing an exhaustive list of graphical representations of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations w ∈𝔖5, 𝔖6.

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖6

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖

Deodhar [Geom. Dedicata 36, no. 1 (1990)] introduced the defect statistic on subexpressions of reduced expressions in the symmetric group 𝔖n to construct an...

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖₆

Published Online: Jun 18, 2022

Page range: 68 - 74

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0011

Keywords
Hecke algebra, Kazhdan-Lusztig basis, planar network

© 2022 Ashton Datko et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖6

Published Online: Jun 18, 2022

Page range: 68 - 74

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0011

KeywordsHecke algebra, Kazhdan-Lusztig basis, planar network

© 2022 Ashton Datko et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖₆

Keywords
Hecke algebra, Kazhdan-Lusztig basis, planar network