Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $$ \mathcal{N} $$ = 4 SYM theory
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep08(2019)149
Abstract: Abstract The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group U(N ) are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from… read more here.
Keywords: connected correlators; wilson loops; theory; note generating ... See more keywords
Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep11(2019)170
Abstract: Abstract We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just… read more here.
Keywords: genus one; generating functions; string dualities; one fibered ... See more keywords
Hamiltonian braids via generating functions
Sign Up to like & getrecommendations! Published in 2024 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-025-03870-z
Abstract: Given a compactly supported Hamiltonian diffeomorphism of the plane, one can define a generating function for it. In this paper, we show how generating functions retain information about the braid type of collections of fixed… read more here.
Keywords: braids via; via generating; hamiltonian braids; generating functions ... See more keywords
The rank-generating functions of upho posets
Sign Up to like & getrecommendations! Published in 2022 at "Discrete Mathematics"
DOI: 10.1016/j.disc.2021.112629
Abstract: Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that the principal order filter at every vertex is isomorphic to the whole poset. Well-known examples include k-array… read more here.
Keywords: rank generating; upho posets; generating functions; functions upho ... See more keywords
Generating functions for finite sums involving higher powers of binomial coefficients: Analysis of hypergeometric functions including new families of polynomials and numbers
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.05.015
Abstract: The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized… read more here.
Keywords: powers binomial; binomial coefficients; sums involving; new families ... See more keywords
Continued fractions and q-series generating functions for the generalized sum-of-divisors functions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2017.05.023
Abstract: Abstract We construct new continued fraction expansions of Jacobi-type J-fractions in z whose power series expansions generate the ratio of the q-Pochhammer symbols, ( a ; q ) n / ( b ; q )… read more here.
Keywords: series generating; generating functions; series; divisors functions ... See more keywords
Generating functions for generalized Hermite polynomials associated with parabolic cylinder functions
Sign Up to like & getrecommendations! Published in 2019 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2019.1697695
Abstract: ABSTRACT In this article, we first give some basic properties of generalized Hermite polynomials associated with parabolic cylinder functions. We next use Weisnerś group theoretic method and operational rules method to establish new generating functions… read more here.
Keywords: generalized hermite; associated parabolic; generating functions; hermite polynomials ... See more keywords
Donaldson-Thomas invariants, torus knots, and lattice paths
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review D"
DOI: 10.1103/physrevd.98.026022
Abstract: In this paper, we find and explore the correspondence between quivers, torus knots, and combinatorics of counting paths. Our first result pertains to quiver representation theory—we find explicit formulas for classical generating functions and Donaldson-Thomas… read more here.
Keywords: generating functions; invariants torus; lattice paths; thomas invariants ... See more keywords
Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review. E"
DOI: 10.1103/physreve.103.l040103
Abstract: The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has… read more here.
Keywords: initial conditions; cumulant generating; symmetric exclusion; functions tracer ... See more keywords
Generating Functions in the Knapsack Problem
Sign Up to like & getrecommendations! Published in 2018 at "Doklady Mathematics"
DOI: 10.1134/s1064562418050198
Abstract: The knapsack problem with Boolean variables and a single constraint is considered. Combinatorial formulas for calculating and estimating the cardinality of the set of feasible solutions and the values of the functional in various cases… read more here.
Keywords: generating functions; problem; knapsack problem; functions knapsack ... See more keywords
On the generating functions of products mixing two k-Fibonacci and other sequences
Sign Up to like & getrecommendations! Published in 2025 at "Georgian Mathematical Journal"
DOI: 10.1515/gmj-2025-2030
Abstract: Abstract We present a simple and general formula for the generating function of the product of two polynomial sequences, based on lesser-known results. This approach is largely of a matricial nature. We describe how to… read more here.
Keywords: two fibonacci; functions products; generating functions; fibonacci sequences ... See more keywords