6 citations · 22 across the 25 of their papers we have counts for
31 papers
Tadpole Nahm sum as a Wronskian
Shane Chern, Chanh Tran, Tanay Wakhare
We show that the tadpole Nahm sum is essentially a specialization of a series studied by Bartlett and Warnaar. This overlooked connection was first discovered by the internal model…
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…
A divisor generating -series and cumulants arising from random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +2
Uchimura, in 1987, introduced a probability generating function for a random variable and using properties of this function he discovered an interesting -series identity. He…
Iterated Entropy Derivatives and Binary Entropy Inequalities
Tanay Wakhare
We embark on a systematic study of the -th derivative of , where is the binary entropy and are integers. Our motiv…
Prompts have evil twins
Rimon Melamed, Lucas H. McCabe, Tanay Wakhare +3
We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language mode…
Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Parth Chavan, Sarth Chavan, Christophe Vignat +1
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its s…
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…
Taylor coefficients of the Jacobi function
Tanay Wakhare, Christophe Vignat
We extend some results recently obtained by Dan Romik about the Taylor coefficients of the theta function to the case of an arbitrary va…
Romik's Conjecture for the Jacobi Theta Function
Tanay Wakhare
Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point . He then conjectured that the Taylor coefficients $d(…
The Inverse Eigenvalue Problem for Linear Trees
Tanay Wakhare, Charles R. Johnson
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a l…
Analytic Continuation for Multiple Zeta Values using Symbolic Representations
Lin Jiu, Tanay Wakhare, Christophe Vignat
We introduce a symbolic representation of -fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., suc…
A symbolic approach to the poly-Bernoulli numbers
T. Wakhare, C. Vignat
We present a symbolic representation for the poly-Bernoulli numbers. This allows us to prove several new iterated integral representations for the poly-Bernoulli numbers, including…
A Generalized Newton-Girard Identity
Tanay Wakhare
We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these ident…
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…
Structural properties of multiple zeta values
Tanay Wakhare, Christophe Vignat
We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complemen…
Settling some sum suppositions
Tanay Wakhare, Christophe Vignat
We solve multiple conjectures by Byszewski and Ulas about the sum of base digits function. In order to do this, we develop general results about summations over the sum of digi…
On a generalization of the Rogers generating function
Howard S. Cohl, Roberto S. Costas-Santos, Tanay Wakhare
We derive a generalized Rogers generating function and corresponding definite integral, for the continuous -ultraspherical polynomials by applying its connection relation and ut…
Special values of -gamma products
Tanay Wakhare
We consider products of -gamma functions with rational arguments, and prove several -generalizations of recent works concerning products of gamma functions. In particular, we…
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…
Some generating functions for q-polynomials
Howard S. Cohl, Roberto S. Costas-Santos, Tanay V. Wakhare
We obtain q-analogues of the Sylvester, Cesàro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.
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…