IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 25 Jan 2021 17:35:46 GMT2021-01-25T17:35:46Z10241The Schützenberger involution over Dyck pathshttp://hdl.handle.net/11585/534993Titolo: The Schützenberger involution over Dyck paths
Abstract: We describe a map Γ from the set of Dyck paths of given
semilength to itself that is the analog of the Schützenberger involution
on standard Young tableaux. Afterwards, we examine the behavior
of Γ with respect to Knuth’s correspondence between pairs
of standard Young tableaux of the same shape with at most two
rows and Dyck paths. Finally, we exploit the previous results to
describe a bijection between the set of 321-avoiding centrosymmetric
permutations of even length and the set of 321-avoiding involutions
of the same length.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11585/5349932016-01-01T00:00:00ZMotzkin and Catalan Tunnel Polynomialshttp://hdl.handle.net/11585/651881Titolo: Motzkin and Catalan Tunnel Polynomials
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11585/6518812018-01-01T00:00:00ZPermutations and Pairs of Dyck Pathshttp://hdl.handle.net/11585/133221Titolo: Permutations and Pairs of Dyck Paths
Abstract: We define a map nu between the symmetric group S_n and the set of pairs of Dyck paths of semilength n. We show that the map nu is injective when restricted to the set of 1234-avoiding permutations and characterize the image of this map.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/1332212013-01-01T00:00:00ZYoung tableaux and k-matchings in finite posetshttp://hdl.handle.net/11585/11049Titolo: Young tableaux and k-matchings in finite posets
Abstract: We present a recursive procedure that directly associates a Young tableau to an arbitrary finite poset with a linear extension, where no a priori information about its Ferrers shape is required.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11585/110492004-01-01T00:00:00ZTwo Permutation Classes Enumerated by the Central Binomial Coefficientshttp://hdl.handle.net/11585/134215Titolo: Two Permutation Classes Enumerated by the Central Binomial Coefficients
Abstract: We define a map between the set of permutations that avoid either the four patterns 3214, 3241, 4213, 4231 or 3124, 3142, 4123, 4132, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the statistics “number of ascents”, “number of left-to-right maxima”, “first element”, and “position of the maximum element”.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/1342152013-01-01T00:00:00ZAn algorithmic approach to maximal unions of chains in a partially ordered sethttp://hdl.handle.net/11585/11121Titolo: An algorithmic approach to maximal unions of chains in a partially ordered set
Abstract: We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a finite partially ordered set P for every positive integer k. As a consequence, we obtain an algorithmic proof of Greene's Duality Theorem on the relations between the cardinalities of maximal unions of chains and antichains in a finite poset.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/111212005-01-01T00:00:00ZThe descent statistic on involutions is not log-concavehttp://hdl.handle.net/11585/62761Titolo: The descent statistic on involutions is not log-concave
Abstract: We establish a combinatorial connection
between the sequence $(i_{n,k})$ counting the involutions on $n$
letters with $k$ descents and the sequence $(a_{n,k})$ enumerating
the semistandard Young tableaux on $n$ cells with $k$ symbols.
This allows us to show that the sequences $(i_{n,k})$ are not
log-concave for some values of $n$, hence answering a conjecture
due to F. Brenti.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11585/627612009-01-01T00:00:00ZAscending runs in permutations and valued Dyck pathshttp://hdl.handle.net/11585/668442.1Titolo: Ascending runs in permutations and valued Dyck paths
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11585/668442.12019-01-01T00:00:00ZSome permutations on Dyck wordshttp://hdl.handle.net/11585/566812Titolo: Some permutations on Dyck words
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11585/5668122016-01-01T00:00:00ZThe Eulerian numbers on restricted centrosymmetric permutationshttp://hdl.handle.net/11585/102099Titolo: The Eulerian numbers on restricted centrosymmetric permutations
Abstract: We study the descent distribution over the set of centrosymmetric permu- tations that avoid a pattern of length 3. In the most puzzling case, namely, τ = 123 and n even, our main tool is a bijection that associates a Dyck pre􏰜x of length 2n to every centrosymmetric permutation in S_{2n} that avoids 123.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11585/1020992010-01-01T00:00:00Z