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A
classification of nonzero skew immaculate functions
Sarah Mason and Tianhao Xie |
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Vol. 19 (2026), No. 1, 87–105
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Abstract |
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We present conditions under which the skewed version of immaculate noncommutative symmetric functions are nonzero. We are motivated by the quest to determine when the matrix definition of a skew immaculate function aligns with the Hopf algebraic definition. We describe a necessary condition for a skew immaculate function to include a nonzero term, as well as a sufficient condition for there to be at least one nonzero term that survives any cancellation. We bring in several classical theorems such as the pigeonhole principle from combinatorics and Hall’s matching theorem from graph theory to prove our theorems. |
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Keywords
symmetric functions, NSym, immaculate functions,
Jacobi–Trudi formula, Hall's matching theorem
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Mathematical Subject Classification
Primary: 05E05
Secondary: 05A05
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Milestones
Received: 8 March 2024
Revised: 6 August 2024
Accepted: 8 August 2024
Published: 25 January 2026
Communicated by Joshua Cooper
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Authors |
| Sarah Mason | |
| Department of Mathematics Wake Forest University Winston-Salem, NC United States |
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| Tianhao Xie | |
| Department Of Mathematics Wake Forest University Winston-Salem, NC United States |
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| © 2026 MSP (Mathematical Sciences Publishers). |
