Results 11 to 20 of about 165 (24)
Forum of Mathematics, SigmaVertically symmetric alternating sign matrices (VSASMs) of order $2n+1$ are known to be equinumerous with lozenge tilings of a hexagon with side lengths $2n+2,2n,2n+2,2n,2n+2,2n$ and a central triangular hole of size $2$ that exhibit
Ilse Fischer, Hans Höngesberg
doaj +1 more source
On $t$-extensions of the Hankel determinants of certain automatic sequences
, 2014 In 1998, Allouche, Peyri\`ere, Wen and Wen considered the Thue--Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integral numbers.
Fu, Hao, Han, Guo-Niu
core +1 more source
Bijective enumerations of $\Gamma$-free 0-1 matrices
, 2017 We construct a new bijection between the set of $n\times k$ $0$-$1$ matrices with no three $1$'s forming a $\Gamma$ configuration and the set of $(n,k)$-Callan sequences, a simple structure counted by poly-Bernoulli numbers.
Bényi, Beáta, Nagy, Gábor V.
core +1 more source
An inversion metric for reduced words
, 2018 We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes ranked with ...
Assaf, Sami
core +1 more source
Bounded Littlewood identity related to alternating sign matrices
Forum of Mathematics, SigmaAn identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that alternating sign ...
Ilse Fischer
doaj +1 more source
Two permutation classes enumerated by the central binomial coefficients [PDF]
, 2013 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.
Barnabei, Marilena +2 more
core +1 more source
A generalization of the "probléme des rencontres" [PDF]
, 2018 In this paper, we study a generalization of the classical \emph{probl\'eme des rencontres} (\emph{problem of coincidences}), consisting in the enumeration of all permutations $ \pi \in \SS_n $ with $k$ fixed points, and, in particular, in the ...
Capparelli, Stefano +3 more
core
Pattern Popularity in 132-Avoiding Permutations [PDF]
, 2012 The popularity of a pattern p is the total number of copies of p within all permutations of a set. We address popularity in the set of 132-avoidng permutations.
Rudolph, Kate
core
Pattern Count on Multiply Restricted Permutations [PDF]
, 2013 Previous work has studied the pattern count on singly restricted permutations. In this work, we focus on patterns of length 3 in multiply restricted permutations, especially for double and triple pattern-avoiding permutations. We derive explicit formulae
Zhao, Alina F. Y.
core
Ascent Sequences Avoiding Pairs of Patterns [PDF]
, 2014 Ascent sequences were introduced by Bousquet-Melou et al. in connection with (2+2)-avoiding posets and their pattern avoidance properties were first considered by Duncan and Steingrímsson.
Baxter, Andrew M, Pudwell, Lara
core +4 more sources