Results 51 to 60 of about 2,046 (100)

On the number of vertices of each rank in phylogenetic trees and their generalizations [PDF]

Discrete Mathematics & Theoretical Computer Science, 2016
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
Miklós Bóna
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A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs [PDF]

, 2006
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor.
Friedland, Shmuel, Levy, Daniel
core   +1 more source

On a generalization of derangement polynomials and numbers

Demonstratio Mathematica
In T. Kim, D. S. Kim, and D. V. Dolgy, Probabilistic derangement numbers and polynomials, Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, 2529188, Kim-Kim defined the probabilistic derangement polynomials and numbers and found some properties of those ...
Yun Sang Jo, Park Jin-Woo
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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
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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
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Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou (2018) to be in bijection with pyramidal sequences of consecutive ...
Ioannis Michos, Christina Savvidou
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Distribution of sets of descent tops and descent bottoms on restricted permutations [PDF]

Discrete Mathematics & Theoretical Computer Science
In 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
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Growing and Destroying Catalan-Stanley Trees [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
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Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of ...
Dun Qiu, Jeffrey Remmel
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Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
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