1 citations · 1 across the 15 of their papers we have counts for
17 papers
Enumerating separable derangements
Robert Dougherty-Bliss, Alejandro B. Galván, Michaela A. Polley +1
We give a polynomial-time algorithm to compute the number of separable derangements of . This algorithm is based on a generating function technique which tracks permutat…
In How Many Ways can a Rectangle be Rectangled?
Pablo Blanco, Robert Dougherty-Bliss, Natalya Ter-Saakov +1
There are ways to tile a rectangle with rectangular tiles (of any length, of course they all must have width ), but in how many ways can you tile a $100 \…
Necklaces, subset sums, and cyclic permutations
Robert Dougherty-Bliss, Sergi Elizalde
It is a well known that, for odd , the number of subsets of the sum of whose elements is divisible by equals the number of binary necklaces of length .…
Cutting 4 by grids into two congruent pieces
Robert Dougherty-Bliss, Natalya Ter-Saakov, Doron Zeilberger
In the March 2025 issue of Pour la Science, Jean-Paul Delahaye described a wonderful solution to the following problem: How many ways can you divide a 3 by 2n rectangle into two co…
The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices
Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov +1
A chessboard has the property that every row and every column has as many white squares as black squares. In this mostly methodological note, we address the problem of counting suc…
The Comma Sequence is Finite in Other Bases
Robert Dougherty-Bliss, Natalya Ter-Saakov
The comma sequence (1, 12, 35, 94, ...) is the lexicographically earliest sequence such that the difference of consecutive terms equals the concatenation of the digits on either si…
Creating Decidable Diophantine Equations
Robert Dougherty-Bliss, Charles Kenney, Doron Zeilberger
Generalizing an argument of Matiyasevich, we illustrate a method to generate infinitely many diophantine equations whose solutions can be completely described by linear recurrences…
Hardinian Arrays
Robert Dougherty-Bliss, Manuel Kauers
In 2014, R.H. Hardin contributed a family of sequences about king-moves on an array to the On-Line Encyclopedia of Integer Sequences (OEIS). The sequences were recently noticed in…
Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes
Robert Dougherty-Bliss, Doron Zeilberger
We use Experimental Mathematics and Symbolic Computation (with Maple), to search for lots and lots of Perrin- and Lucas- style primality tests, and try to sort the wheat from the c…
Gosper's algorithm and Bell numbers
Robert Dougherty-Bliss
Computers are good at evaluating finite sums in closed form, but there are finite sums which do not have closed forms. Summands which do not produce a closed form can often be ``fi…
The Meta-C-finite Ansatz
Robert Dougherty-Bliss
The Fibonacci numbers satisfy the famous recurrence . The theory of C-finite sequences ensures that the Fibonacci numbers whose indices are divisible b…
Exploring General Apéry Limits via the Zudilin-Straub t-transform
Robert Dougherty-Bliss, Doron Zeilberger
Inspired by a recent beautiful construction of Armin Straub and Wadim Zudilin, that 'tweaked' the sum of the powers of the -th row of Pascal's triangle, getting instead…
Experimenting with Apery Limits and WZ pairs
Robert Dougherty-Bliss, Doron Zeilberger
This article, dedicated with admiration in memory of Jon and Peter Borwein, illustrates by example, the power of experimental mathematics, so dear to them both, by experimenting wi…
Integral Recurrences from A to Z
Robert Dougherty-Bliss
George Boros and Victor Moll's masterpiece "Irresistible Integrals" does well to include a suitably-titled appendix, "The Revolutionary WZ Method," which gives a brief overview of…
Tweaking the Beukers Integrals In Search of More Miraculous Irrationality Proofs A La Apery
Robert Dougherty-Bliss, Christoph Koutschan, Doron Zeilberger
There are only aleph-zero rational numbers, while there are 2 to the power aleph-zero real numbers. Hence the probability that a randomly chosen real number would be rational is 0.…
Enumerating Restricted Dyck Paths with Context-Free Grammars
AJ Bu, Robert Dougherty-Bliss
The number of Dyck paths of semilength is famously , the th Catalan number. This fact follows after noticing that every Dyck path can be uniquely parsed according to a…
Automatic Conjecturing and Proving of Exact Values of Some Infinite Families of Infinite Continued Fractions
Robert Dougherty-Bliss, Doron Zeilberger
Inspired by the recent pioneering work, dubbed "The Ramanujan Machine" by Raayoni et al. (arXiv:1907.00205), we (automatically) [rigorously] prove some of their conjectures regardi…