Results 151 to 160 of about 523,591 (296)
Partial Steiner Triple Systems With an Almost Parallel Class Missing Any Given Point
Journal of Combinatorial Designs, EarlyView.ABSTRACT We say that a hypergraph is factor critical if it has no 1‐factor but deletion of any vertex results in a hypergraph that has a 1‐factor. We show that any factor‐critical hypergraph of order n $n$ has at least n $n$ edges, and that for all integers k > 1 $k\gt 1$ and n > 1 $n\gt 1$ with n ≡ 1 ( mod k ) $n\equiv 1({\rm{mod}}\,k)$ there exists a
Darryn Bryant +2 more
wiley +1 more source
Catalan Bounds for Symmetric Strength‐Two Orthogonal Arrays
Journal of Combinatorial Designs, EarlyView.ABSTRACT A Hamming shell construction is a two‐level array obtained by taking every binary vector of a given Hamming weight a prescribed number of times, for each weight in turn. Such arrays are invariant under all permutations of the factors, and they are strength‐two orthogonal arrays exactly when the multiplicities satisfy three linear constraints ...
Ruwan C. Karunanayaka
wiley +1 more source
Theorems on the zeros of linear differential operators
Известия высших учебных заведений. Поволжский регион: Физико-математические наукиBackground. Differential connections between solutions of systems of differential equations play a significant role in mathematics and mathematical physics. The operators and algebras of differential symmetry of linear homogeneous systems of differential
A.I. Fomin, V.I. Titarenko
doaj +1 more source
External Analogy in Inductive Theorem Proving
, 1997 . This paper investigates analogy-driven proof plan construction in inductive theorem proving. Given a proof plan of a source theorem, we identify constraints of second-order mappings that enable a replay of the source plan to produce a similar plan for ...
Erica Melis, Jon Whittle
core
Updating the Incomplete MOLS Table for v $v$ up to 100
Journal of Combinatorial Designs, EarlyView.ABSTRACT Incomplete transversal designs have wide application in the construction of other designs such as transversal designs, block designs, frames, statistical designs, and Latin rectangles. Other areas where they are used include telecommunications and network codes, obtaining physically unclonable functions, frequency hopping sequences and ...
R. Julian R. Abel +2 more
wiley +1 more source
Formal verification of bioinformatics software using model checking and theorem proving. [PDF]
Brief BioinformWeerasena H +3 more
europepmc +1 more source
Automated Theorem Proving using the TPTP Process Instruction Language
The TPTP (Thousands of Problems for Theorem Provers) World is a well established infrastructure for Automated Theorem Proving (ATP). In the context of the TPTP World, the TPTP Process Instruction (TPI) language provides capabilities to input, output and ...
Geoff Sutcliffe, Muhammad Nassar
core +1 more source
On Odd Covers of Cliques and Disjoint Unions
Journal of Graph Theory, EarlyView.ABSTRACT Babai and Frankl posed the “odd cover problem” of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order n $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always ⌈ n / 2 ⌉ $\lceil n/2\rceil $ or ⌈ n /
Calum Buchanan +7 more
wiley +1 more source
Explicit 3‐colorings for Exponential Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +2 more
wiley +1 more source