Abstract
In this paper, the bijection between k-rook placements on a Ferrers board and k-matchings in the associated bipartite graph is extended to a bijection between k-file placements and certain fractional matchings. Using the latter bijection, a new interpretation is given for the normal ordering coefficients in the shift algebra. Several further results concerning normal ordering in the shift algebra are derived.
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Communicated by Bridget Tenner.
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Schork, M. File Placements, Fractional Matchings, and Normal Ordering. Ann. Comb. 26, 857–871 (2022). https://doi.org/10.1007/s00026-022-00599-y
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DOI: https://doi.org/10.1007/s00026-022-00599-y
Keywords
- Ferrers boards
- Rook placements
- File placements
- Weyl algebra
- Shift algebra
- Normal ordering
- Generalized Stirling numbers