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Variance of a strongly additive function defined on random permutations
Inspired by unfading popularity of the Turán–Kubilius inequality for additive number theoretic functions within the last decades, we examine the...
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A sharp inequality for the variance with respect to the Ewens sampling formula
We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the...
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Nearly subadditive sequences
We show that the de Bruijn–Erdős condition for the error term in their improvement of Fekete's Lemma is not only sufficient but also necessary in the...
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On the number of generalized Sidon sets
A set A of nonnegative integers is called a Sidon set if there is no Sidon 4-tuple, i.e., ( a, b, c, d ) in A with a + b = c + d and { a, b }∩{ c, d } = ø;....
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Counting SET-Free Sets
We consider the following counting problem related to the card game SET: how many k-element SET-free sets are there in an n-dimensional SET deck? ...
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The Number of Triple Systems Without Even Cycles
For k ⩾ 4, a loose k -cycle C k is a hypergraph with distinct edges e 1 , e 2 , …, e k such that consecutive edges (modulo k ) intersect in exactly one...
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On the Number of Bases of Almost All Matroids
For a matroid M of rank r on n elements, let b ( M ) denote the fraction of bases of M among the subsets of the ground set with cardinality r . We show...
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On the Number of Unary-Binary Tree-Like Structures with Restrictions on the Unary Height
We investigate various classes of Motzkin trees as well as lambda-terms for which we derive asymptotic enumeration results. These classes are defined...
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Fringe analysis of plane trees related to cutting and pruning
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a...
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Completely Effective Error Bounds for Stirling Numbers of the First and Second Kinds via Poisson Approximation
We provide completely effective error estimates for Stirling numbers of the first and second kinds, denoted by s ( n , m ) and S ( n , m ), respectively....
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Intervals of Permutation Class Growth Rates
We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θ B ≈ 2:35526, and that it...
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Analysis of Bidirectional Ballot Sequences and Random Walks Ending in Their Maximum
Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice...
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Square-root cancellation for the signs of Latin squares
Let L ( n ) be the number of Latin squares of order n , and let L even ( n ) and L odd ( n ) be the number of even and odd such squares, so that L ( n )= L ...
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The height of multiple edge plane trees
Multi-edge trees as introduced in a recent paper of Dziemiańczuk are plane trees where multiple edges are allowed. We first show that d -ary...
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On the maximum number of points in a maximal intersecting family of finite sets
Paul Erdős and LászlÓ Lovász proved in a landmark article that, for any positive integerk, up to isomorphism there are only finitely many maximal...
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Powers of Hamilton cycles in pseudorandom graphs
We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph G ...
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Restrictive Patterns of Combinatorial Structures via Comparative Analysis
Asymptotic probabilities of decomposable combinatorial structures with a fortiori prescribed properties are studied as the sizes unboundedly...
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On the share of closed
IL formulas which are also inGL Normal forms for wide classes of closed
IL formulas were given in Čačić and Vuković (Math Commun 17:195–204,2012 ). Here we quantify asymptotically,...