Exceedingly deranging!

Mantaci, Roberto; Rakotondrajao, Fanja

doi:10.1016/s0196-8858(02)00531-6

Cited by 14 publications

(7 citation statements)

References 7 publications

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“…Proof. Mantaci and Rakotondrajao (see [6]) have proved the identity d o n,k − d e n,k = (−1) n using recursive argument. Applying this with the Corollary 4.5, we get the desired formula.…”

Section: Excedance Distribution Over Padsmentioning

confidence: 99%

Parity alternating permutations starting with an odd integer

Kebede,

Rakotondrajao

2021

Preprint

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A Parity Alternating Permutation of the set [n] = {1, 2, . . . , n} is a permutation with even and odd entries alternatively. We deal with parity alternating permutations having an odd entry in the first position, PAPs. We study the numbers that count the PAPs with even as well as odd parity. We also study a subclass of PAPs being derangements as well, Parity Alternating Derangements (PADs). Moreover, by considering the parity of these PADs we look into their statistical property of excedance.

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Section: Excedance Distribution Over Padsmentioning

confidence: 99%

Parity alternating permutations starting with an odd integer

Kebede,

Rakotondrajao

2021

Preprint

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“…A similar result for derangements in S n was given by Chapman [7], i.e., the number of even and odd derangements in S n differs by n − 1. This result has been generalized by introducing the concept of "excedance" in the work of Mantaci and Rakotondrajao [13].…”

Section: Signed Excedances On Type B Derangementsmentioning

confidence: 99%

Excedance Numbers for the Permutations of Type B

Zhao

2013

Electron. J. Combin.

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This work provides a study on the multidistribution of type $B$ excedances, fixed points and cycles on the permutations of type $B$. We derive the recurrences and closed formulas for the distribution of signed excedances on type $B$ permutations as well as derangements via combinatorial construction. Based on this result, we obtain the recurrence and generating function for the signed excedance polynomial and disclose some relationships with Euler numbers and Springer numbers, respectively.

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“…This pattern is not new; for example, you can find the sequences e n and o n in the OEIS [12]. A bijective proof using a conjugation argument can be found in [2], and the recent paper [9] offers two more proofs based on an analysis of Table 3. Number of even and odd derangements for n ≤ 7.…”

Section: The Parity Of Derangements and C-derangementsmentioning

confidence: 99%

Moving Faces to Other Places: Facet Derangements

Gordon¹,

McMahon²

2010

The American Mathematical Monthly

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Derangements are a popular topic in combinatorics classes. We study a generalization to face derangements of the n-dimensional hypercube. These derangements can be classified as odd or even, depending on whether the underlying isometry is direct or indirect, providing a link to abstract algebra. We emphasize the interplay between the geometry, algebra and combinatorics of these sequences, with lots of pretty pictures.

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Exceedingly deranging!

Cited by 14 publications

References 7 publications

Parity alternating permutations starting with an odd integer

Parity alternating permutations starting with an odd integer

Excedance Numbers for the Permutations of Type B

Moving Faces to Other Places: Facet Derangements

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