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- W251058549 abstract "Given a coprime pair (m;n) of positive integers, rational Catalan numbers 1 m+n m+n m;n counts two combinatorial objects: rational (m;n)-Dyck paths are lattice paths in the m n rectangle that never go below the diagonal; (m;n)-cores are parti- tions with no hook length equal to m or n. Anderson established a bijection between (m;n)-Dyck paths and (m;n)-cores. We dene a new transformation, called rank com- plement, on rational Dyck paths. We show that rank complement corresponds to con- jugation of (m;n)-cores under Anderson's bijection. This leads to: i) a new approach to characterizing n-cores; ii) a simple approach for counting the number of self-conjugate (m;n)-cores; iii) a proof of the equivalence of two conjectured combinatorial sum for- mulas, one over rational (m;n)-Dyck paths and the other over (m;n)-cores, for rational Catalan polynomials." @default.
- W251058549 created "2016-06-24" @default.
- W251058549 creator A5049446116 @default.
- W251058549 date "2015-04-08" @default.
- W251058549 modified "2023-09-27" @default.
- W251058549 title "RANK COMPLEMENT OF RATIONAL DYCK PATHS AND CONJUGATION OF (m;n)-CORE PARTITIONS" @default.
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