The permutation class Av(4213,2143) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its ...
David Bevan
doaj +1 more source
Repeatable patterns and the maximum multiplicity of a generator in a reduced word [PDF]
We study the maximum multiplicity \(\mathcal{M}(k,n)\) of a simple transposition \(s_k=(k \: k+1)\) in a reduced word for the longest permutation \(w_0=n \: n-1 \: \cdots \: 2 \: 1\), a problem closely related to much previous work on sorting networks ...
Gao, Yibo +4 more
core +1 more source
Proofs of Conjectures about Pattern-Avoiding Linear Extensions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation.
Colin Defant
doaj +1 more source
Some collapsibility results for n-dimensional contingency tables
Collapsibility, Conditional independence, Contingency table, Log-linear model, Möbius inversion, Simpson’s paradox, Strict collapsibility, Primary 62H17, Secondary 62E99, Secondary 05A05,
P. Vellaisamy, V. Vijay
core +1 more source
The 26 Wilf-equivalence classes of length five quasi-consecutive patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$.
Evan Chen, Shyam Narayanan
doaj +1 more source
A new algorithm for computing the Geronimus transformation with large shifts [PDF]
, 2009 39 pages, no figures.-- MSC2000 codes: 15A21, 15A23, 05A05, 05B25.-- Full-text paper available Open access at the journal site.Article in press.A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence ...
Deaño Cabrera, Alfredo +8 more
core +1 more source
Key-avoidance for alternating sign matrices [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM.
Mathilde Bouvel +2 more
doaj +1 more source
Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered partitions of {1,..,n} whose block sizes are determined by R. These are the
Robert A. Proctor, Matthew J. Willis
doaj +1 more source
Decompositions of packed words and self duality of Word Quasisymmetric Functions [PDF]
By Foissy's work, the bidendriform structure of the Word Quasisymmetric Functions Hopf algebra (WQSym) implies that it is isomorphic to its dual. However, the only known explicit isomorphism due to Vargas does not respect the bidendriform structure. This
Mlodecki, Hugo
core +1 more source
Distribution of sets of descent tops and descent bottoms on restricted permutations [PDF]
Discrete Mathematics & Theoretical Computer ScienceIn this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations.
Alexander Burstein
doaj +1 more source