Results 11 to 20 of about 120 (120)
A bijective proof of Kohnert's rule for Schubert polynomials [PDF]
, 2022 Kohnert proposed a formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the diagram of a permutation.
Assaf, Sami H.
core +1 more source
Counting lattice paths by crossings and major index I: the corner-flipping bijections [PDF]
, 2022 We solve two problems regarding the enumeration of lattice paths in \(\mathbb{Z}^2\) with steps \((1,1)\) and \((1,-1)\) with respect to the major index, defined as the sum of the positions of the valleys, and to the number of certain crossings.
Elizalde, Sergi
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On the Okounkov-Olshanski formula for standard tableaux of skew shapes [PDF]
, 2022 The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape.
H. Morales, Alejandro H. +1 more
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Toppleable permutations, excedances and acyclic orientations [PDF]
, 2022 Recall that an excedance of a permutation \(\pi\) is any position \(i\) such that \(\pi_i > i\). Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it gets
Hathcock, Daniel +2 more
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Some convolution identities for Frobenius-Euler polynomials [PDF]
, 2017 In this paper, by applying the generating function methods and summation transform techniques, we establish some new convolution identities for the Frobenius-Euler polynomials. It turns out that some well-known results are obtained as special cases.
Jing Pan +3 more
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Flip-sort and combinatorial aspects of pop-stack sorting [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural,
Andrei Asinowski +2 more
doaj +1 more source
1974 conjecture of Andrews on partitions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 21, Page 1097-1104, 2004., 2004 The case k = a of the 1974 conjecture of Andrews on two partition functions Aλ,k,a(n) and Bλ,k,a(n) was proved by the first author and Sudha (1993) and the case k = a + 1 was established by the authors (2000). In this paper, we prove that the conjecture is false and give a revised conjecture for a particular case when λ is even.
Padmavathamma, M. R. Salestina
wiley +1 more source
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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MacMahon’s statistics on higher-dimensional partitions
Forum of Mathematics, Sigma, 2023 We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers.
Alimzhan Amanov, Damir Yeliussizov
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A quantum field theoretical representation of Euler‐Zagier sums
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 127-148, 2002., 2002 We establish a novel representation of arbitrary Euler‐Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders.
Uwe Müller, Christian Schubert
wiley +1 more source