6 citations · 22 across the 25 of their papers we have counts for
10 papers · 1 filter
On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
Shane Chern, Chanh Tran, Tanay Wakhare
We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type , thereby yielding a conjectural fermionic formula due to…
Extremal Graphs for a Spectral Inequality on Edge-Disjoint Spanning Trees
Sebastian M. Cioabă, Anthony Ostuni, Davin Park +3
Liu, Hong, Gu, and Lai proved if the second largest eigenvalue of the adjacency matrix of graph with minimum degree satisfies ,…
The Toughness of Kneser Graphs
Davin Park, Anthony Ostuni, Nathan Hayes +4
The \textit{toughness} of a graph is a measure of its connectivity that is closely related to Hamiltonicity. Brouwer proved the lower bound on the t…
The Proportion of Trees that are Linear
Tanay Wakhare, Eric Wityk, Charles R. Johnson
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for…
Restricted -Stirling Numbers and their Combinatorial Applications
Beáta Bényi, Miguel Méndez, José L. Ramírez +1
We study set partitions with distinguished elements and block sizes found in an arbitrary index set . The enumeration of these -partitions leads to the introduction o…
Hyper -ary expansions and Stern polynomials
Tanay Wakhare, Caleb Kendrick, Matthew Chung +8
We study a recently introduced base polynomial analog of Stern's diatomic sequence, which generalizes Stern polynomials of Klavar, Dilcher, Ericksen, Mansour, Stolarsky, and ot…
Refinements of the Bell and Stirling numbers
Tanay Wakhare
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associ…
A continuous analogue of lattice path enumeration
T. Wakhare, C. Vignat, Q. -N. Le +1
Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts c…
Woon's tree and sums over compositions
C. Vignat, T. Wakhare
This article studies sums over all compositions of an integer. We derive a generating function for this quantity, and apply it to several special functions, including various gener…
Special classes of -bracket operators
Tanay Wakhare
We study the -bracket operator of Bloch and Okounkov when applied to and . We use these…