Combinatorial analysis. (Matrix problems, choice theory)

DOI10.1007/BF01089193zbMath0507.05001MaRDI QIDQ1837183

V. E. Tarakanov, N. V. Nosov, V. N. Sachkov

Publication date: 1983

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

Latin squarestransversalspermanentsmatroidsSperner collections

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Exact enumeration problems, generating functions (05A15) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Permutations, words, matrices (05A05) Orthogonal arrays, Latin squares, Room squares (05B15)

Cites Work

• A Note on Tutte's Unimodular Representation Theorem
• Maximal Representable Subfamilies
• Weak Maps of Combinatorial Geometries
• The Enumeration of Generalized Double Stochastic Nonnegative Integer Square Matrices
• Weight Enumeration and the Geometry of Linear Codes
• Subpermanents of doubly stochastic matrices^†
• Embedding Orthogonal Partial Latin Squares
• Permanents of special classes of doubly stochastic matrices
• On Bases of Independence Structures Intersecting in a Set of Prescribed Cardinality
• INTERSECTION THEOREMS FOR SETS OF SUBSETS OF A FINITE SET
• Finding the circuits of a matroid
• The Forbidden Minors of Binary Clutters
• The invariance of elementary symmetric functions
• Doubly stochastic matrices with dominant p-minors
• A note on permanents
• Intersection Theorems for Systems of Sets
• An Intersection Theorem for a Collection of Families of Subsets of a Finite Set
• Disjoint Common Transversals and Exchange Structures
• The Asymptotic Behaviour of Equidistant Permutation Arrays
• An Algorithm for the Permanent of Circulant Matrices
• On a conjecture of M. Marcus and H. Minc
• The Broken-Circuit Complex
• Permanental Pairs of Doubly Stochastic Matrices
• COLOURING, PACKING AND THE CRITICAL PROBLEM
• BICIRCULAR MATROIDS
• Permanent Semigroups
• NECESSARY CONDITIONS FOR THE COMPLETION OF PARTIAL LATIN SQUARES
• A study of the van der Waerden conjecture and its generalizations
• The Missing Axiom of Matroid Theory is Lost Forever
• An Elementary Proof of Johnson–Dulmage–Mendelsohn's Refinement of Birkhoff's Theorem on Doubly Stochastic Matrices
• A note on matrices with constant permanental minors
• Evaluation of Permanents
• Monotonicity of permanents of doubly stochastic matrices
• Semimodular Functions and Combinatorial Geometries
• On Double Diagonal and Cross Latin Squares
• Doubly whose stochastic matrices squares leave the permanent invariant
• An Upper Bound for the Permanent of a Fully Indecomposable Matrix
• A Note on the van Der Waerden Permanent Conjecture
• On the inequality Σxiyi ≥ 1/nΣxi·Σyi and the van der Waerden permanent conjecture
• A lower bound for the order of a partial transversal in a latin square
• Incomplete Diagonals of Latin Squares
• Permanents of cyclic (0,1) matrices
• On Lower Bounds for Permanents of (0, 1) Matrices
• Conversion of the Permanent into the Determinant
• On Completing Latin Rectangles
• On the extreme points of a certain convex polytope
• A Simplified Form for Nearly Reducible and Nearly Decomposable Matrices
• A Lower Bound for the Permanent of a (0, 1)-Matrix
• On the Permanent of a Certain Class of (0, 1)-Matrices
• On the Foundations of Combinatorial Theory II. Combinatorial Geometries
• Asymptotics and random matrices with row-sum and column sum-restrictions
• Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices
• The Asymptotic Number of Latin Rectangles
• On intersecting families of finite sets
• On a conjecture of Erdős and Renyi
• Matrix factorizations of determinants and permanents
• On permanents of circulants
• The structure of Sperner k-families
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• Matroids and linking systems
• Projections and weak maps in combinatorial geometries
• A simple method for constructing doubly diagonalized Latin squares
• On the relation between the determinant and the permanent
• Some results on Sperner families
• Enumeration of arrays by column rises
• On the existence of uncountably many matroidal families
• Asymptotic evaluation of the number of latin rectangles
• Matroid representation over GF(3)
• The asymptotic number of (0,1)-matrices with zero permanent
• The asymptotic number of non-negative integer matrices with given row and column sums
• Symmetric matrices with given row sums
• On permanents of (1,-1)-matrices
• Study of the permanent conjecture and some of its generalizations
• Transversals of latin squares and their generalizations
• The number of 9x9 Latin squares
• Truncations of principal geometries
• The proof of a conjecture of G. O. H. Katona
• On the nonreconstructibility of combinatorial geometries
• Matrices satisfying the van der Waerden conjecture
• Doubly stochastic matrices with minimal permanents
• A number-theoretic function related to Latin squares
• Permanents of 0,1-matrices
• Two algorithms for matroids
• The Euler circuit theorem for binary matroids
• Common transversals
• On the number of systems of distinct representatives in an independence structure
• Extremal properties of collections of subsets containing no two sets and their union
• A strengthened form of Tutte's characterization of regular matroids
• Einige Sätze über gemeinsame Transversalen zweier Mengenfamilien
• On permanents and the zeros of rook polynomials
• Some combinatorial properties of centrosymmetric matrices
• Doubly stochastic matrices which have certain diagonals with constant sums
• On finite Delta-systems. II
• Convex polyhedra of doubly stochastic matrices. I: Applications of the permanent function
• A construction for equidistant permutation arrays of index one
• A combinatorial perspective on the Radon convexity theorem
• On the extreme points of the polytope of symmetric matrices with given row sums
• Convex sets of some doubly stochastic matrices
• Matroids with given restrictions and contractions
• An \(n\times n\) Latin square has a transversal with at least \(n-\sqrt n\) distinct symbols
• A simple proof that every matroid is an intersection of fundamental transversal matroids
• Rectangular arrays
• Connected matroids with the smallest Whitney numbers
• The solution to a matroid problem of Knuth
• Orientability of matroids
• The matroids with the max-flow min-cut property
• Orthogonal systems
• Enumeration of arrays of a given size
• Some results about the Chvatal conjecture
• Combinatorial properties of systems of sets
• Construction of Knut Vik designs
• On the chromatic number of regular matroids
• On strong joins and pushout of combinatorial geometries
• The distribution of 1-widths of (0,1)-matrices
• Real permanental roots of doubly stochastic matrices
• On the completion of partial squares
• Functors of the category of combinatorial geometries and strong maps
• A short proof of Minc's conjecture
• Some inequalities for multidimensional (0,1)-matrices
• Maximal sets of permutations constructed from projective planes
• Vector representable matroids of given rank with given automorphism group
• Non-singular 0-1 matrices with constant row and column sums
• Families of finite sets satisfying a union condition
• Combinatorial problems on the existence of large submatrices. II
• A Sperner-type theorem for families of finite sets
• The asymptotic number of labeled graphs with given degree sequences
• The Higgs factorization of a geometric strong map
• On Reid's characterization of the ternary matroids
• The Radon transforms of a combinatorial geometry, I
• Geometries simpliciales unimodulaires
• (0,1)-matrices with minimal permanents
• Bounds for certain permanents and determinants
• Convex sets of doubly stochastic matrices
• A characterization of convertible (0,1)-matrices
• A new class of finite cyclic permanent groups
• On the minimum of the permanent of a doubly stochastic matrix
• A conjecture and some problems on permanents
• Extensions of classical matrix inequalities
• A lower bound for the permanent on \(U_ n(k,k)\)
• Remarks on the van der Waerden conjecture. II
• The asymptotic number of integer stochastic matrices
• A class of counterexamples on permanents
• Counterexamples to conjectures of Ryser and de Oliveira
• Some notes on the van der Waerden conjecture
• Positive diagonals of \(\pm 1\)-matrices
• Embedding Incomplete Latin Squares
• Permanent Preservers on the Space of Doubly Stochastic Matrices
• The Permanent Function
• Some Results on Doubly Stochastic Matrices
• Permanents of doubly stochastic matrices with fixed zero pattern
• An Affine Representation for Transversal Geometries
• Non‐Algebraic Matroids exist
• Families of finite sets satisfying an intersection condition

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