Parity-alternating permutations and successions

• Autorzy: Augustine Munagi
• Języki publikacji: EN

Abstrakty

EN

The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions - adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations.

Słowa kluczowe

EN

Parity-alternating permutation; Succession block; Circular permutation

Kategorie tematyczne

• 05A05: Permutations, words, matrices
• 05A15: Exact enumeration problems, generating functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 9
• Strony: 1390-1402

Daty

wydano

2014-09-01

online

2014-05-08

Twórcy

autor

Augustine Munagi

• University of the Witwatersrand

Bibliografia

• [1] Andrews G.E., The Theory of Partitions, Encyclopedia of Mathematics and its Applications, 2, Addison-Wesley, Reading, 1976
• [2] Knopfmacher A., Munagi A., Wagner S., Successions in words and compositions, Ann. Comb., 2012, 16(2), 277–287 http://dx.doi.org/10.1007/s00026-012-0131-z
• [3] Moser W.O.J., Abramson M., Generalizations of Terquem’s problem, J. Combinatorial Theory, 1969, 7(2), 171–180 http://dx.doi.org/10.1016/S0021-9800(69)80052-9
• [4] Munagi A.O., Alternating subsets and permutations, Rocky Mountain J. Math., 2010, 40(6), 1965–1977 http://dx.doi.org/10.1216/RMJ-2010-40-6-1965
• [5] Munagi A.O., Alternating subsets and successions, Ars Combin., 2013, 110, 77–86
• [6] Riordan J., Permutations without 3-sequences, Bull. Amer. Math. Soc., 1945, 51, 745–748 http://dx.doi.org/10.1090/S0002-9904-1945-08439-0
• [7] Tanimoto S., Parity alternating permutations and signed Eulerian numbers, Ann. Comb., 2010, 14(3), 355–366 http://dx.doi.org/10.1007/s00026-010-0064-3
• [8] Tanny S.M., Permutations and successions, J. Combinatorial Theory Ser. A, 1976, 21(2), 196–202 http://dx.doi.org/10.1016/0097-3165(76)90063-7

Identyfikatory

DOI

10.2478/s11533-014-0421-2