Bounded Littlewood identity related to alternating sign matrices
Forum of Mathematics, SigmaAn identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that alternating sign ...
Ilse Fischer
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Continued fractions using a Laguerre digraph interpretation of the Foata-Zeilberger bijection and its variants [PDF]
In the combinatorial theory of continued fractions, the Foata-Zeilberger bijection and its variants have been extensively used to derive various continued fractions enumerating several (sometimes infinitely many) simultaneous statistics on permutations ...
Deb, Bishal
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The combinatorics of a tree-like functional equation for connected chord diagrams [PDF]
, 2023 We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating functions of two ...
Nabergall, Lukas
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Restricted lonesum matrices [PDF]
, 2018 Lonesum matrices are matrices that are uniquely reconstructible from their row and column sum vectors. These matrices are enumerated by the poly-Bernoulli numbers; a sequence related to the multiple zeta values with a rich literature in number theory.
Bényi, Beáta
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Topological recursion for fully simple maps from ciliated maps [PDF]
We solve a conjecture from the first and third authors that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy topological recursion for the exchanged spectral curve \((y, x)\), making use of the ...
Garcia-Failde, Elba +5 more
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A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux [PDF]
, 2021 Lusztig's fake degree is the generating polynomial for the major index of standard Young tableaux of a given shape. Results of Springer (1974) and James & Kerber (1984) imply that, mysteriously, its evaluation at a \(k\)-th primitive root of unity ...
Pfannerer, Stephan
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Grass(mannian) trees and forests: Variations of the exponential formula, with applications to the momentum amplituhedron [PDF]
, 2023 The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size.
Moerman, Robert, Williams, Lauren K.
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Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants [PDF]
, 2012 MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the ...
Savic, Natasa +2 more
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The log-convexity of the poly-Cauchy numbers
, 2017 In 2013, Komatsu introduced the poly-Cauchy numbers, which generalizeCauchy numbers. Several generalizations of poly-Cauchy numbers have been con-sidered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In
Komatsu, Takao +3 more
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Generalized Stirling permutations and forests: Higher-order Eulerian and Ward numbers [PDF]
, 2014 20 pags.; 4 figs.; Mathematics Subject Classifications: 05A05, 05A15, 05C30We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests.
Sánchez Villaseñor, Eduardo Jesús +8 more
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