The paper explains a method for finding the number of solutions to a system of multivariate polynomial inequalities over a finite field and applies it to find formulas for the number of contiguous sup…

This paper proves that a majority of filled-in Sudoku grids require a logarithmic fraction of cells to be filled by clues, and constructs grids requiring 18 and 80 clues for 9x9 and 16x16 Sudoku, resp…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The authors prove that the solution-search problem for Ice Walk puzzle is ASP-complete by reducing Hamiltonian cycles in a maximum-degree-3 spanning subgraph of a rectangular grid graph to Ice Walk so…

The paper develops an explicit multi-linear polynomial form for binary polynomial optimization problems after eliminating a subset of variables, allowing for characterization of new special classes wi…

This paper investigates the benefits of generating multiple solutions in each generation for Evolutionary Diversity Optimisation (EDO) and proposes efficient methods to achieve it.

This paper shows #P-completeness for several graph counting problems using a new technique.

The paper provides the conjectured solution for the generating function of k-convex polyominoes, based on analysis of generated enumeration data.

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

This paper investigates the closeness of singularity for $n imes n$ unimodular matrices, specifically for $(2k+1)$-ary and $(k+1)$-ary cases of $4 imes 4$ nonnegative unimodular matrices.

This paper presents two algorithms using the Newton-Raphson method to calculate the floor of y**(1/m) for natural integer numbers y > 2 and m > 1, which can be used to determine if y is an integer pow…

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.

This paper introduces new algorithms for finding prime numbers up to a given bound, achieving a speedup of log N over the sieve of Eratosthenes.

This paper introduces and implements variants of the symmetric lexicographic symmetric-subset reverse search framework for enumerating symmetric feasible subsets of a finite set, applying it to cocirc…

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

The paper re-examines the Parking Permit Problem using the primal-dual scheme, obtaining simple algorithms with superior performance guarantees and providing near-matching lower bounds.