Results 61 to 70 of about 11,854 (238)
History of Catalan numbers [PDF]
, 2014 We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.Comment: 10 ...
Pak, Igor
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On the sub-permutations of pattern avoiding permutations
, 2014 There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees.
Disanto, Filippo, Wiehe, Thomas
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C-Finite Sequences and Riordan Arrays
MathematicsMany prominent combinatorial sequences, such as the Fibonacci, Lucas, Pell, Jacobsthal and Tribonacci sequences, are defined by homogeneous linear recurrence relations with constant coefficients.
Donatella Merlini
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Abundant Neighborhoods, Two‐Sided Markets, and Maximal Matchings
Naval Research Logistics (NRL), Volume 72, Issue 7, Page 1022-1035, October 2025.ABSTRACT I introduce a new graph‐theoretic property called abundant neighborhoods. This property is motivated by studying the thickness of economic markets. A vertex is, roughly, guaranteed to match if and only if it has an abundant neighborhood.
Muhammad Maaz
wiley +1 more source
Strong External Difference Families and Classification of α‐Valuations
Journal of Combinatorial Designs, Volume 33, Issue 9, Page 343-356, September 2025.ABSTRACT One method of constructing ( a 2 + 1 , 2 , a , 1 )‐SEDFs (i.e., strong external difference families) in Z a 2 + 1 makes use of α‐valuations of complete bipartite graphs K a , a. We explore this approach and we provide a classification theorem which shows that all such α‐valuations can be constructed recursively via a sequence of “blow‐up ...
Donald L. Kreher +2 more
wiley +1 more source
The local $h$-vector of the cluster subdivision of a simplex [PDF]
, 2012 The cluster complex $\Delta (\Phi)$ is an abstract simplicial complex, introduced by Fomin and Zelevinsky for a finite root system $\Phi$. The positive part of $\Delta (\Phi)$ naturally defines a simplicial subdivision of the simplex on the vertex set of
Athanasiadis, Christos A. +1 more
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Proof of George Andrews's and David Robbins's q-TSPP Conjecture
, 2012 The conjecture that the orbit-counting generating function for totally symmetric plane partitions can be written as an explicit product formula, has been stated independently by George Andrews and David Robbins around 1983.
Kauers, Manuel +2 more
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Three Open Problems in Enumerative Combinatorics [PDF]
, 2023 Firdous Ahmad Mala
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Enumeration and Construction of Row‐Column Designs
Journal of Combinatorial Designs, Volume 33, Issue 9, Page 357-372, September 2025.ABSTRACT We computationally completely enumerate a number of types of row‐column designs up to isotopism, including double, sesqui, and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO‐arrays. We calculate autotopism group sizes for the designs we generate.
Gerold Jäger +3 more
wiley +1 more source
Thom series of contact singularities [PDF]
, 2010 Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic ...
Fehér, L. M., Rimányi, R.
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