Chessboard complexes indomitable

R.T. Zivaljevic; S.T. Vrecica

RECORD

Chessboard complexes indomitable

S.T. Vrecica, R.T. Zivaljevic

Combinatorics · Submitted 18 Nov 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO].

how it is stated · asserted 1.00 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,963 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO]. Our method also yields some new cases of "constrained Tverberg thereom" in the sense of Hell, including a simple colored Radon's theorem for d+3 points in R^d. This is a final version of the paper with improved presentation, corrected typos and added references.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO].	contribution 0.98	0.89	0.53	asserted 1.00
s1	Our method also yields some new cases of "constrained Tverberg thereom" in the sense of Hell, including a simple colored Radon's theorem for d+3 points in R^d.	result 0.65	0.93	0.23	asserted 0.98
s2	This is a final version of the paper with improved presentation, corrected typos and added references.	background 0.64	0.75	0.02	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO]. Our method also yields some new cases of "constrained Tverberg thereom" in the sense of Hell, including a simple colored Radon's theorem for d+3 points in R^d. This is a final version of the paper with improved presentation, corrected typos and added references.

Human review

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How the literature uses it

2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We present a geometric version of a recent beautiful proof by Blagojevi\'c, Matschke, and Ziegler, avoiding a direct use of topological methods.

A geometric proof of the colored Tverberg theorem · 0.83

Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper

We follow the basic strategy of the degree-theoretic proof in [ref] .

A geometric proof of the colored Tverberg theorem · Introduction · 1.00

What it cites · 6 sentences without a confident label

Compares with 1 paper

Let us compare Theorem [ref] to the original result of Blagojević and Ziegler [ref] .

Optimal bounds for the colored Tverberg problem · The case $s_1=…=s_k=2r-1$ · 1.00

Cites as background 2 papers

The reader is referred to [ref] for very interesting new results of this type, in the context of general Tverberg-Vrećica problem [ref] .

Optimal bounds for a colorful Tverberg--Vrecica type problem · Combinatorial geometry on vector bundles · 0.92
Chessboard (simplicial) complexes and their relatives have been for decades an important theme of topological combinatorics with often unexpected applications in group theory, representation theory, commutative algebra, Lie theory, computational geometry, algebraic topology, and combinatorics, see [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] .

Symmetric Homology of Algebras · Introduction · 1.00

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