# Parity-alternating permutations and successions

Open Mathematics (2014)

- Volume: 12, Issue: 9, page 1390-1402
- ISSN: 2391-5455

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topAugustine Munagi. "Parity-alternating permutations and successions." Open Mathematics 12.9 (2014): 1390-1402. <http://eudml.org/doc/269101>.

@article{AugustineMunagi2014,

abstract = {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.},

author = {Augustine Munagi},

journal = {Open Mathematics},

keywords = {Parity-alternating permutation; Succession block; Circular permutation; parity-alternating permutation; succession block; circular permutation},

language = {eng},

number = {9},

pages = {1390-1402},

title = {Parity-alternating permutations and successions},

url = {http://eudml.org/doc/269101},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Augustine Munagi

TI - Parity-alternating permutations and successions

JO - Open Mathematics

PY - 2014

VL - 12

IS - 9

SP - 1390

EP - 1402

AB - 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.

LA - eng

KW - Parity-alternating permutation; Succession block; Circular permutation; parity-alternating permutation; succession block; circular permutation

UR - http://eudml.org/doc/269101

ER -

## References

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- [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 Zbl1206.05006
- [5] Munagi A.O., Alternating subsets and successions, Ars Combin., 2013, 110, 77–86 Zbl1301.05024
- [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 Zbl0060.02902
- [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 Zbl1233.05217
- [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 Zbl0339.05004

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