1 citations · 3 across the 8 of their papers we have counts for
12 papers
Raised -Dyck paths
Paul Drube
Raised -Dyck paths are a generalization of -Dyck paths that may both begin and end at a nonzero height. In this paper, we develop closed formulas for the number of raised …
Colored Motzkin Paths of Higher Order
Isaac DeJager, Madeleine Naquin, Frank Seidl +1
Motzkin paths of order- are a generalization of Motzkin paths that use steps , , and for every positive integer . We further gener…
Generalized Path Pairs and Fuss-Catalan Triangles
Paul Drube
Path pairs are a modification of parallelogram polyominoes that provide yet another combinatorial interpretation of the Catalan numbers. More generally, the number of path pairs of…
Oriented Local Moves and Divisibility of the Jones Polynomial
Paul Drube, Puttipong Pongtanapaisan
For any virtual link that may be decomposed into a pair of oriented -tangles and , an oriented local move of type is a replacement of wi…
Set-Valued Young Tableaux and Product-Coproduct Prographs
Paul Drube, Maxwell Krueger, Ashley Skalsky +1
Standard set-valued Young tableaux are a generalization of standard Young tableaux where cells can contain unordered sets of integers, with the added condition that every integer a…
Set-Valued Tableaux & Generalized Catalan Numbers
Paul Drube
Standard set-valued Young tableaux are a generalization of standard Young tableaux in which cells may contain more than one integer, with the added conditions that every integer at…
Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers
Paul Drube
An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Suc…
Annular Non-Crossing Matchings
Paul Drube, Puttipong Pongtanapaisan
It is well known that the number of distinct non-crossing matchings of half-circles in the half-plane with endpoints on the x-axis equals the Catalan number . Thi…
Inversions of Semistandard Young Tableaux
Paul Drube
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau column-standard. An -invert…
Generalized Catalan Numbers and the Enumeration of Planar Embeddings
Jonathan E. Beagley, Paul Drube
The Raney numbers are a two-parameter generalization of the Catalan numbers that were introduced by Raney in his investigation of functional composition patterns \cite…
Combinatorics of Tableau Inversions
Jonathan E. Beagley, Paul Drube
A tableau inversion is a pair of entries in row-standard tableau that lie in the same column of yet lack the appropriate relative ordering to make column-standard. An $…
Generalized Skein Modules of Surfaces
Jeffrey Boerner, Paul Drube
Frobenius extensions play a central role in the link homology theories based upon the sl(n) link variants, and each of these Frobenius extensions may be recast geometrically via a…