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On the combinatorics of derangements and related permutations
Highlights- Provide a bijection combinatorial proof for the facts that The number of derangements of length n equals the number of permutations of length n that have ...
AbstractA derangement is a permutation in which no entry is at its original position. The number of derangements of [ n ] is called the “derangement number” or “de Montmort number”, and is denoted by D n. The sequence { D n } enumerates, in ...
Combinatorics of Unique Maximal Factorization Families (UMFFs)
Special Issue on StringologySuppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ$^+$ has a unique maximal factorization over W. The classic circ-UMFF is the set of ...
Combinatorics of Unique Maximal Factorization Families (UMFFs)
Special Issue on StringologySuppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ$^+$ has a unique maximal factorization over W. The classic circ-UMFF is the set of ...