SelectedWorks - Andrew V. Sills

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Selected Works of Andrew V. Sills

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Andrew V. Sills is a Professor in the Department of Mathematical Science at Georgia Southern University. He joined Georgia Southern in 2007.

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About Andrew V. Sills

Andrew V. Sills is a Professor in the Department of Mathematical Science at Georgia Southern University. He joined Georgia Southern in 2007.

An Invitation to the Rogers–Ramanujan Identities

Department of Mathematical Sciences Faculty Bookshelf (2017)

Andrew V. Sills

Book Summary: The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over ...

Ghost Series and a Motivated Proof of the Andrews–Bressoud ...

Journal of Combinatorial Theory, Series A (2017)

Shashank Kanade, James Lepowsky, Matthew C. Russell and Andrew Sills

We present what we call a “motivated proof” of the Andrews–Bressoud partition identities for even moduli. A “motivated proof” of ...

Parts and Subword Patterns in Compositions

Journal of Combinatorics and Number Theory (2017)

Brian Hopkins, Mark Shattuck, Andrew V. Sills, Thotsaporn Thanatipanonda, et al.

We find relationships between subword patterns and residue classes of parts in the set of integer compositions of a given ...

A Formula for the Partition Function That "Counts"

Annals of Combinatorics (2016)

Yuriy Choliy and Andrew V. Sills

We derive a combinatorial multisum expression for the number D(n, k) of partitions of n with Durfee square of order ...

The Minimal Number of Subtrees of a Tree

Graphs and Combinatorics (2015)

Andrew V. Sills and Hua Wang

In this note, we consider the trees (caterpillars) that minimize the number of subtrees among trees with a given degree ...

Odd Fibbinary Numbers and the Golden Ratio

Fibonacci Quarterly (2014)

Linus Lindroos, Andrew Sills and Hua Wang

The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the ...

Contribution to Book

The Apostles and Brothers of Jesus

The Tomb of Jesus and His Family?: Exploring Ancient Jewish Tombs Near Jerusalem’s Walls (2013)

Excerpt: The Talpiot tomb, a tomb excavated outside Jerusalem in 1980 and brought to worldwide public attention in 2007, contained ...

Rademacher's Infinite Partial Fractions Conjecture is (Almost Certainly) False

Journal of Difference Equations and Applications (2013)

Andrew Sills and Doron Zeilberger

In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that ...

On a Pair of Identities from Ramanujan's Lost Notebook

Annals of Combinatorics (2012)

James McLaughlin and Andrew Sills

Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some ...

On the Maximal Wiener Index and Related Questions

Discrete Applied Mathematics (2012)

Andrew Sills and Hua Wang

The Wiener index of a graph is the sum of the distances between all pairs of vertices. It has been ...

Formulæ for the Number of Partitions of n into at ...

Advances in Applied Mathematics (2012)

Andrew Sills and Doron Zeilberger

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely ...

Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities

Proceedings of the Conference on Partitions, q-Series, and Modular Forms (2012)

Sylvie Corteel, Carla D. Savage and Andrew Sills

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that ...

Compositions, Partitions, and Fibonacci Numbers

Fibonacci Quarterly (2011)

A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the ...

Polynomial Generalizations of Two-Variable Ramanujan Type Identities

Electronic Journal of Combinatorics (2011)

James McLaughlin and Andrew Sills

We provide finite analogs of a pair of two-variable q-series identities from Ramanujan's lost notebook and a companion identity.

Hybrid Proofs of the q-Binomial Theorem and Other Identities

Electronic Journal of Combinatorics (2011)

Dennis Eichhorn, James McLaughlin and Andrew Sills

We give "hybrid" proofs of the q-binomial theorem and other identities. The proofs are "hybrid" in the sense that we ...

On an Identity of Gessel and Stanton and the New ...

Advances in Applied Mathematics (2011)

Carla D. Savage and Andrew Sills

We show that an identity of Gessel and Stanton [I. Gessel, D. Stanton, Applications of q-Lagrange inversion to basic hypergeometric ...

Rademacher-Type Formulas for Restricted Partition and Overpartition Functions

Ramanujan Journal (2010)

A collection of Hardy-Ramanujan-Rademacher type formulas for restricted partition and overpartition functions is presented, framed by several biographical anecdotes.

Rademacher-Type Formulas for Partitions and Overpartitions

International Journal of Mathematics and Mathematical Sciences (2010)

A Rademacher-type convergent series formula which generalizes the Hardy-Ramanujan-Rademacher formula for the number of partitions of n and the Zuckerman ...

Some Implications of Chu's 10ψ10 Generalization of Bailey's ...

Online Journal of Analytic Combinatorics (2010)

James McLaughlin, Andrew Sills and Peter Zimmer

Lucy Slater used Bailey's 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of ...

Contribution to Book

Towards an Automation of the Circle Method

Gems in Experimental Mathematics in Contemporary Mathematics (2010)

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for ﬁnding ...

Lifting Bailey Pairs to WP-Bailey Pairs

Discrete Mathematics (2009)

James McLaughlin, Andrew Sills and Peter Zimmer

A pair of sequences (αn(a,k,q),βn(a,k,q)) such that α0(a,k,q)=1 and βn(a,k,q)=∑nj=0 (k/a;q)n−j (k;q)n+j / (q;q)n−j (aq;q)n+j αj (a,k,q) is termed a ...

Rogers-Ramanujan Computer Searches

Journal of Symbolic Compuation (2009)

James McLaughlin, Andrew Sills and Peter Zimmer

We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of ...

Some More Identities of Rogers-Ramanujan Type

Ramanujan Journal (2009)

Douglas Bowman, James McLaughlin and Andrew Sills

In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result ...

Combinatorics of Ramanujan-Slater Type Identities

Integers (2009)

James McLaughlin and Andrew Sills

We provide the missing member of a family of four q-series identities related to the modulus 36, the other members ...

Ramanujan–Slater Type Identities Related to the Moduli 18 and ...

Journal of Mathematical Analysis and Applications (2008)

James McLaughlin and Andrew Sills

We present several new families of Rogers–Ramanujan type identities related to the moduli 18 and 24. A few of the ...