Results 1 to 10 of about 73 (73)
Enumeration of Stack-Sorting Preimages via a Decomposition Lemma [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 We give three applications of a recently-proven "Decomposition Lemma," which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$.
Colin Defant
doaj +1 more source
Enumeration of Dumont permutations avoiding certain four-letter patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 In this paper, we enumerate Dumont permutations of the fourth kind avoiding or containing certain permutations of length 4. We also conjecture a Wilf-equivalence of two 4-letter patterns on Dumont permutations of the first kind.
Alexander Burstein, Opel Jones
doaj +1 more source
The number of distinct adjacent pairs in geometrically distributed words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for $1~\leq~j~\leq~n$ with $p+q=
Margaret Archibald +5 more
doaj +1 more source
Enumerating two permutation classes by the number of cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We enumerate permutations in the two permutation classes $\text{Av}_n(312, 4321)$ and $\text{Av}_n(321, 4123)$ by the number of cycles each permutation admits. We also refine this enumeration with respect to several statistics.
Kassie Archer
doaj +1 more source
Two examples of Wilf-collapse [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Two permutation classes, the X-class and subpermutations of the increasing oscillation are shown to exhibit an exponential Wilf-collapse. This means that the number of distinct enumerations of principal subclasses of each of these classes grows much more
Michael Albert +2 more
doaj +1 more source
The Hurwitz action in complex reflection groups [PDF]
, 2022 We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family \(G(m, p, n)\) of complex reflection groups.
Lewis, Joel Brewster, Wang, Jiayuan
core +1 more source
Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by
Hanna Mularczyk
doaj +1 more source
The homogenized Linial arrangement and Genocchi numbers [PDF]
, 2022 We study the intersection lattice of a hyperplane arrangement recently introduced by Hetyei who showed that the number of regions of the arrangement is a median Genocchi number.
Wachs, Michelle L., +3 more
core +1 more source
Certificate complexity and symmetry of nested canalizing functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity.
Yuan Li, Frank Ingram, Huaming Zhang
doaj +1 more source
The combinatorics of a tree-like functional equation for connected chord diagrams [PDF]
, 2023 We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating functions of two ...
Nabergall, Lukas
core +1 more source